I have studied a bit of Zen, "the sound of one hand clapping" one of the things I remember most. Breathing is the key to all meditations.
I presume that hand clapping was a practice in feeling the vibrations? This is a good body awareness test; "where do you hear/feel those vibrations?".
Yes, breathing plays a big role in meditation for two important reasons, to get in touch with your body (your self!) and to filter out distracting thoughts. It takes time to get -more- control over your mind, it's far from easy.
Here's a nice mantra,