user11674: Is there a specific reason why the breath is used as the object of anapanasati or to be more precise: Why did the Buddha chose the breath. 
Does it mean then that in daily life our main object should also be the breath?

user8157: The Buddha did not chose the breath. Instead, the breath chose the Buddha. 
When the mind surrenders or abandons craving, the sense organs/objects of sight, sound, smelling, tasting, external touching & pre-occupation with thinking disengage. 
What remains, as the most coarse or gross sense object, is the breathing. 
When the mind is quiet, empty & free, i.e., when "mindfulness is established to the fore", the breathing automatically, without choosing, becomes the natural object of meditation. 
This is the meaning of Anapanasati, namely, 'mindfulness with breathing' rather than 'awareness of breathing'. 
Those who attempt to practise 'awareness of breathing' may experience some samatha (calmness) but will not progress very far because the path of the Buddha is the path of abandoning craving. 

user12107: The first good thing about the breath is that while you are alive, it is always available. Another good thing is that it is internal, not an external object. The purpose of this kind of meditation is to train the mind to be able to focus single pointedly. Ultimately, this ability can be used to meditate on the emptiness of self and all phenomena, eventually resulting in a direct perception of emptiness, AKA, Nirvana.

user295: Does it mean then that in daily life our main object should also be the breath?
In the context of Buddhist meditation, there are 40 subjects of meditation (Kammaṭṭhāna). These are divided into

Samatha for concentration and mastery over the mind
Vipassanā for wisdom

The Noble Eightfold Path has 3 subdivisions:

morality (Śīla) - developed though recollection of morality (Śīla)
mastery over the mind (Samadhi) - developed through Samatha
wisdom (Paññā) - developed through Vipassanā

Anapanasati is one of the meditation techniques under Vipassanā to develop the 4 Satipatthana. Vipassanā is easier to develop in daily life as Samatha requires longer hours of meditation to develop concentration (Samadhi). Anapanasati helps develop both Samadhi and Paññā at the same time, but this is not the only technique at your disposal.

user16966: Seems that moderators are expecting a particular style in these answers, and so deleted my initial answer. I'll rephrase...
The reason that the breath is the most important meditation object is that unlike other objects they are always available. For example, you might forget your TM mantra or misplace your mandala. Other objects of meditation, such as decaying corpses, aren't usually freely available in the UK either :-)

11674: <p>Is there a specific reason why the breath is used as the object of anapanasati or to be more precise: Why did the Buddha chose the breath. </p>

<p>Does it mean then that in daily life our main object should also be the breath?</p>
 8157: <p>The Buddha did not chose the breath. Instead, the breath chose the Buddha. </p>

<p>When the mind surrenders or abandons craving, the sense organs/objects of sight, sound, smelling, tasting, external touching &amp; pre-occupation with thinking disengage. </p>

<p>What remains, as the most coarse or gross sense object, is the breathing. </p>

<p>When the mind is quiet, empty &amp; free, i.e., when "<em>mindfulness is established to the fore</em>", the breathing automatically, without choosing, becomes the natural object of meditation. </p>

<p>This is the meaning of Anapanasati, namely, '<em>mindfulness with breathing</em>' rather than '<em>awareness of breathing</em>'. </p>

<p>Those who attempt to practise '<em>awareness of breathing</em>' may experience some <em>samatha</em> (calmness) but will not progress very far because the path of the Buddha is the path of abandoning craving. </p>
 12107: <p>The first good thing about the breath is that while you are alive, it is always available. Another good thing is that it is internal, not an external object. The purpose of this kind of meditation is to train the mind to be able to focus single pointedly. Ultimately, this ability can be used to meditate on the emptiness of self and all phenomena, eventually resulting in a direct perception of emptiness, AKA, Nirvana.</p>
 295: <p><strong>Does it mean then that in daily life our main object should also be the breath?</strong></p>

<p>In the context of Buddhist meditation, there are 40 subjects of meditation (<a href="https://en.wikipedia.org/wiki/Kamma%E1%B9%AD%E1%B9%ADh%C4%81na" rel="nofollow noreferrer">Kammaṭṭhāna</a>). These are divided into</p>

<ul>
<li><a href="https://en.wikipedia.org/wiki/Samatha" rel="nofollow noreferrer">Samatha</a> for concentration and mastery over the mind</li>
<li><a href="https://en.wikipedia.org/wiki/Vipassan%C4%81" rel="nofollow noreferrer">Vipassanā</a> for wisdom</li>
</ul>

<p>The <a href="https://en.wikipedia.org/wiki/Noble_Eightfold_Path" rel="nofollow noreferrer">Noble Eightfold Path</a> has <a href="https://en.wikipedia.org/wiki/Threefold_Training" rel="nofollow noreferrer">3 subdivisions</a>:</p>

<ul>
<li>morality (<a href="https://en.wikipedia.org/wiki/%C5%9A%C4%ABla" rel="nofollow noreferrer">Śīla</a>) - developed though recollection of morality (<a href="https://en.wikipedia.org/wiki/%C5%9A%C4%ABla" rel="nofollow noreferrer">Śīla</a>)</li>
<li>mastery over the mind (<a href="https://en.wikipedia.org/wiki/Samadhi" rel="nofollow noreferrer">Samadhi</a>) - developed through <a href="https://en.wikipedia.org/wiki/Samatha" rel="nofollow noreferrer">Samatha</a></li>
<li>wisdom (<a href="https://en.wikipedia.org/wiki/Praj%C3%B1%C4%81_(Buddhism)" rel="nofollow noreferrer">Paññā</a>) - developed through <a href="https://en.wikipedia.org/wiki/Vipassan%C4%81" rel="nofollow noreferrer">Vipassanā</a></li>
</ul>

<p><a href="https://en.wikipedia.org/wiki/Anapanasati" rel="nofollow noreferrer">Anapanasati</a> is one of the meditation techniques under <a href="https://en.wikipedia.org/wiki/Vipassan%C4%81" rel="nofollow noreferrer">Vipassanā</a> to develop the <a href="https://en.wikipedia.org/wiki/Satipatthana" rel="nofollow noreferrer">4 Satipatthana</a>. <a href="https://en.wikipedia.org/wiki/Vipassan%C4%81" rel="nofollow noreferrer">Vipassanā</a> is easier to develop in daily life as <a href="https://en.wikipedia.org/wiki/Samatha" rel="nofollow noreferrer">Samatha</a> requires longer hours of meditation to develop concentration (<a href="https://en.wikipedia.org/wiki/Samadhi" rel="nofollow noreferrer">Samadhi</a>). <a href="https://en.wikipedia.org/wiki/Anapanasati" rel="nofollow noreferrer">Anapanasati</a> helps develop both <a href="https://en.wikipedia.org/wiki/Samadhi" rel="nofollow noreferrer">Samadhi</a> and <a href="https://en.wikipedia.org/wiki/Praj%C3%B1%C4%81_(Buddhism)" rel="nofollow noreferrer">Paññā</a> at the same time, but this is not the only technique at your disposal.</p>
 16966: <p>Seems that moderators are expecting a particular style in these answers, and so deleted my initial answer. I'll rephrase...</p>

<p>The reason that the breath is the most important meditation object is that unlike other objects they are always available. For example, you might forget your TM mantra or misplace your mandala. Other objects of meditation, such as decaying corpses, aren't usually freely available in the UK either :-)</p>
