user760: I take it that an important claim of secular Buddhism is that the Buddha never actually taught literal rebirth.
What happens during parinibbāna according to secular Buddhism? How is it different from any other death? If there is no difference, how do secular Buddhists explain the very existence of this term? Can any death be called parinibbāna?

user8157: 
I take it that an important claim of secular Buddhism is that the Buddha never actually taught literal rebirth.

'Birth' ('jati') is the production of ideas or views of 'self' or 'beings' ('satta'), as explained in SN 12.2, SN 23.2 and SN 5.10. Therefore, the Buddha certainly taught literal 'rebirth' but this literal rebirth is the literal re-production of ideas & views of 'self' or 'beings' or 'persons'. 

What happens during parinibbāna according to secular Buddhism?

Parinibbana is described in the suttas as the cravingless ending of conscious experience of an arahant (Iti 44; MN 140; SN 22.85; etc), as follows: 

'Here in this very life, all that is experienced, not being delighted in, will be extinguished.'
Iti 44


.

How is it different from any other death?

'Death' ('marana') is the idea that a self or "a being" dies (SN 12.2). Parinibbana is not 'death'. There are many suttas that say an arahant does not experience death (SN 22.85; MN 140; MN 38; etc). 

If there is no difference, how do secular Buddhists explain the very existence of this term? 

Parinibbana is a term used for the peaceful cravingless ending of the life of an arahant. Currently, I do not know the reason why this term is used but I imagine it is possibly used so Arahants & Buddhas are not insulted by applying the word "death" to them and to highlight how the life of an arahant ends peacefully without any craving. The suttas say: 

Dhp 21. Heedfulness is the path to the Deathless. Heedlessness is the path to death. The heedful die not. The heedless are as if dead
  already.

The Buddha-To-Be searched for freedom from "death" (MN 26) yet the question here does not focus on what "death" really is but wants to talk about Nibbana, which is something that will never ever be experienced if what "death" & the "deathless" really are is not discerned. 

Can any death be called parinibbāna?

Death (marana) is not Parinibbana (cravingless ending of consciousness), as explained. Death is a personal self-view while consciousness is merely an impermanent impersonal natural element (dhatu). 
"Death" is the death of beings or selves, as follows: 

Long have you (repeatedly) experienced the death of a mother. The tears you have shed over the death of a mother while transmigrating &
  wandering this long, long time—crying & weeping from being joined with
  what is displeasing, being separated from what is pleasing—are greater
  than the water in the four great oceans.
“Long have you (repeatedly) experienced the death of a father… the death of a brother… the death of a sister… the death of a son… the
  death of a daughter… loss with regard to relatives… loss with regard
  to wealth… loss with regard to disease.
SN 15.3

When life & experience is viewed as merely elements & aggregates, there will be no more "mother", "father", "son", "daughter", etc, and no more "death". 

And what may be said to be subject to death... sorrow... defilement? Spouses & children... men & women slaves... goats & sheep... fowl &
  pigs... elephants, cattle, horses, & mares... gold & silver  are
  subject to death... sorrow... defilement. Subject to death...
  sorrow... defilement are these acquisitions, and one who is tied to
  them, infatuated with them, who has totally fallen for them, being
  subject to birth, seeks what is likewise subject to aging...
  illness... death... sorrow... defilement. This is ignoble search.
MN 26


user16635: A lot of people conflate the concept of 'rebirth' with the concept of 'reincarnation,' but philosophically speaking they are subtly different. Reincarnation implies an eternal essence or being that returns to inhabit a new physical form. Rebirth in the Buddhist sense is actually the opposite: the idea that our unresolved attachments set the ground for the recreation of the five aggregates that constitute a being. 
In that sense, rebirth is like — to use a colloquial analogy — an echo. A sound is sent out and an echo returns; the echo is the same sound sent out again, and a new echo returns. The nature of the sound can change through distortion, clarification, or interference over time, but the process continues until the sound itself is silenced. After that, there are no more echoes. Don't misunderstand; silence can be a powerful thing. A room where everyone is talking is a comfortable jangle of noise, perhaps, but a room where everyone is silent borders on the state of awe. It's merely our attachments to that warm, comfortable, sensuous noise that leads to the echoes that recur.
So if nirvana is the achievement of true silence in our lifetime, parinirvana would be the continuation of that silence after death. Imagine that the whole of Buddhism is the continuation of the silence of the Buddha after his death — a silence that absorbs the noise of others and helps them find silence in their own right — and you'll get a sense for the nature of paranirvana.
Note that I haven't once used the term 'secular,' as though secular Buddhism were something different than 'regular' Buddhism. That's just more noise.

user43: In my understanding, the notion of Nirvana was a nod towards pre-Buddhist (Inc. Jain) ideas of the times. Nirvana was something transcental, something ultimate everyone spoke about but barely anyone could define.
When The Buddha achieved his Breakthrough, he mapped his ideas back to preexisting notions, to make it easier to communicate with people. So Nirvana is a bit tongue-in-cheek term, the so-called Nirvana. The Buddha attained what he himself called "Liberation of mind from suffering through Wisdom", which he equated with the Nirvana everyone at the times were looking for. 
Then, the notion of Parinirvana is an even more ironic gesture. Since "Nirvana in this life" was actualized by not holding on to anything that could create a basis for suffering, death of "someone who is like this" (Tathagata) was the ultimate act of not holding on to anything to the highest degree possible, thus it can be half-jokingly called Super-Nirvana or Parinirvana.
Regular people die while still grasping at things, and so their death leaves an element of regret which then lives on as a negative impulse affecting the lives of people to come.
The Buddha's death is the ultimate act of letting go. It's an act of letting things go on their own course, governed only by Natural Law. The Buddha haven't attempted to stay behind and continue teaching Dharma indefinitely - which would be an act of grasping. Instead, his Parinirvana is an example to all of us Buddhists to not force the right Dharma on everyone, nor be aggressive in teaching and saving people, but to let things play out naturally while helping whenever we can.

760: <p>I take it that an important claim of secular Buddhism is that the Buddha never actually taught literal rebirth.</p>

<p>What happens during parinibbāna according to secular Buddhism? How is it different from any other death? If there is no difference, how do secular Buddhists explain the very existence of this term? Can any death be called parinibbāna?</p>
 8157: <blockquote>
  <p><strong>I take it that an important claim of secular Buddhism is that the Buddha never actually taught literal rebirth.</strong></p>
</blockquote>

<p>'Birth' ('jati') is the production of ideas or views of 'self' or 'beings' ('satta'), as explained in SN 12.2, SN 23.2 and SN 5.10. Therefore, the Buddha certainly taught literal 'rebirth' but this literal rebirth is the literal re-production of ideas &amp; views of 'self' or 'beings' or 'persons'. </p>

<blockquote>
  <p><strong>What happens during parinibbāna according to secular Buddhism?</strong></p>
</blockquote>

<p>Parinibbana is described in the suttas as the cravingless ending of conscious experience of an arahant (Iti 44; MN 140; SN 22.85; etc), as follows: </p>

<blockquote>
  <p><em>'Here in this very life, all that is experienced, not being delighted in, will be extinguished.'</em></p>
  
  <p><em>Iti 44</em></p>
  
  <hr>
</blockquote>

<p>.</p>

<blockquote>
  <p><strong>How is it different from any other death?</strong></p>
</blockquote>

<p>'Death' ('marana') is the idea that a self or "a being" dies (SN 12.2). Parinibbana is not 'death'. There are many suttas that say an arahant does not experience death (SN 22.85; MN 140; MN 38; etc). </p>

<blockquote>
  <p><strong>If there is no difference, how do secular Buddhists explain the very existence of this term?</strong> </p>
</blockquote>

<p>Parinibbana is a term used for the peaceful cravingless ending of the life of an arahant. Currently, I do not know the reason why this term is used but I imagine it is possibly used so Arahants &amp; Buddhas are not insulted by applying the word "death" to them and to highlight how the life of an arahant ends peacefully without any craving. The suttas say: </p>

<blockquote>
  <p><em>Dhp 21. Heedfulness is the path to the Deathless. Heedlessness is the path to death. The heedful die not. The heedless are as if dead
  already.</em></p>
</blockquote>

<p>The Buddha-To-Be searched for freedom from "death" (MN 26) yet the question here does not focus on what "death" really is but wants to talk about Nibbana, which is something that will never ever be experienced if what "death" &amp; the "deathless" really are is not discerned. </p>

<blockquote>
  <p><strong>Can any death be called parinibbāna?</strong></p>
</blockquote>

<p>Death (marana) is not Parinibbana (cravingless ending of consciousness), as explained. Death is a personal self-view while consciousness is merely an impermanent impersonal natural element (dhatu). </p>

<p>"Death" is the death of beings or selves, as follows: </p>

<blockquote>
  <p><em>Long have you (repeatedly) experienced the death of a <strong>mother</strong>. The tears you have shed over the death of a mother while transmigrating &amp;
  wandering this long, long time—crying &amp; weeping from being joined with
  what is displeasing, being separated from what is pleasing—are greater
  than the water in the four great oceans.</em></p>
  
  <p><em>“Long have you (repeatedly) experienced the death of a <strong>father</strong>… the death of a <strong>brother</strong>… the death of a <strong>sister</strong>… the death of a <strong>son</strong>… the
  death of a <strong>daughter</strong>… loss with regard to <strong>relatives</strong>… loss with regard
  to <strong>wealth</strong>… loss with regard to disease.</em></p>
  
  <p><em>SN 15.3</em></p>
</blockquote>

<p>When life &amp; experience is viewed as merely elements &amp; aggregates, there will be no more "mother", "father", "son", "daughter", etc, and no more "death". </p>

<blockquote>
  <p><em>And what may be said to be subject to death... sorrow... defilement? Spouses &amp; children... men &amp; women slaves... goats &amp; sheep... fowl &amp;
  pigs... elephants, cattle, horses, &amp; mares... gold &amp; silver  are
  subject to death... sorrow... defilement. Subject to death...
  sorrow... defilement are these acquisitions, and one who is tied to
  them, infatuated with them, who has totally fallen for them, being
  subject to birth, seeks what is likewise subject to aging...
  illness... death... sorrow... defilement. This is <strong>ignoble</strong> search.</em></p>
  
  <p><em>MN 26</em></p>
</blockquote>
 16635: <p>A lot of people conflate the concept of 'rebirth' with the concept of 'reincarnation,' but philosophically speaking they are subtly different. <em>Reincarnation</em> implies an eternal essence or being that returns to inhabit a new physical form. <em>Rebirth</em> in the Buddhist sense is actually the opposite: the idea that our unresolved attachments set the ground for the recreation of the five aggregates that constitute a being. </p>

<p>In that sense, rebirth is like — to use a colloquial analogy — an echo. A sound is sent out and an echo returns; the echo is the same sound sent out again, and a new echo returns. The nature of the sound can change through distortion, clarification, or interference over time, but the process continues until the sound itself is silenced. After that, there are no more echoes. Don't misunderstand; silence can be a powerful thing. A room where everyone is talking is a comfortable jangle of noise, perhaps, but a room where everyone is silent borders on the state of awe. It's merely our attachments to that warm, comfortable, sensuous noise that leads to the echoes that recur.</p>

<p>So if nirvana is the achievement of true silence in our lifetime, parinirvana would be the continuation of that silence after death. Imagine that the whole of Buddhism is the continuation of the silence of the Buddha after his death — a silence that absorbs the noise of others and helps them find silence in their own right — and you'll get a sense for the nature of paranirvana.</p>

<p>Note that I haven't once used the term 'secular,' as though secular Buddhism were something <em>different</em> than 'regular' Buddhism. That's just more noise.</p>
 43: <p>In my understanding, the notion of Nirvana was a nod towards pre-Buddhist (Inc. Jain) ideas of the times. Nirvana was something transcental, something ultimate everyone spoke about but barely anyone could define.</p>

<p>When The Buddha achieved his Breakthrough, he mapped his ideas back to preexisting notions, to make it easier to communicate with people. So Nirvana is a bit tongue-in-cheek term, the so-called Nirvana. The Buddha attained what he himself called "Liberation of mind from suffering through Wisdom", which he equated with the Nirvana everyone at the times were looking for. </p>

<p>Then, the notion of Parinirvana is an even more ironic gesture. Since "Nirvana in this life" was actualized by not holding on to anything that could create a basis for suffering, death of "someone who is like this" (Tathagata) was the ultimate act of not holding on to anything to the highest degree possible, thus it can be half-jokingly called Super-Nirvana or Parinirvana.</p>

<p>Regular people die while still grasping at things, and so their death leaves an element of regret which then lives on as a negative impulse affecting the lives of people to come.</p>

<p>The Buddha's death is the ultimate act of letting go. It's an act of letting things go on their own course, governed only by Natural Law. The Buddha haven't attempted to stay behind and continue teaching Dharma indefinitely - which would be an act of grasping. Instead, his Parinirvana is an example to all of us Buddhists to not force the right Dharma on everyone, nor be aggressive in teaching and saving people, but to let things play out naturally while helping whenever we can.</p>
