user-1: I'm curious to know: how important is posture during meditation? Could someone meditate on public transport, or while walking in different places? Is there a difference in the necessity of posture between a beginner and an advanced practitioner?

user8157: Posture is extremely important however sitting cross-legged is not important. What is important is having a naturally erect spine so the mind is alert & the breathing can flow unrestricted. 
When sitting in public transport, sit upright, close your eyes & meditate. Completely let go of any self-consciousness that other people are watching you & know what you are doing. Relax & enjoy. 
As for walking meditation, this is something monks do a lot. You should try to learn how to do walking meditation (but not in a busy or dangerous place, such as when crossing a busy street in the city). 

user6999: To answer your question, yes one can meditate anytime anywhere.  The following might be far reaching example, however,  during Buddha's time Ven. Maha Kassapa was an expert in meditation.  As a matter of fact, he was the only person Buddha compared himself to be equal in the ability to enter Jhana at any time any posture.  

-1: <p>I'm curious to know: how important is posture during meditation? Could someone meditate on public transport, or while walking in different places? Is there a difference in the necessity of posture between a beginner and an advanced practitioner?</p>
 8157: <p>Posture is extremely important however sitting cross-legged is not important. What is important is having a naturally erect spine so the mind is alert &amp; the breathing can flow unrestricted. </p>

<p>When sitting in public transport, sit upright, close your eyes &amp; meditate. Completely let go of any self-consciousness that other people are watching you &amp; know what you are doing. Relax &amp; enjoy. </p>

<p>As for walking meditation, this is something monks do a lot. You should try to learn how to do walking meditation (but not in a busy or dangerous place, such as when crossing a busy street in the city). </p>
 6999: <p>To answer your question, yes one can meditate anytime anywhere.  The following might be far reaching example, however,  during Buddha's time Ven. Maha Kassapa was an expert in meditation.  As a matter of fact, he was the <strong>only person</strong> Buddha compared himself to be <strong>equal</strong> in the ability to enter Jhana at any time any posture.  </p>
