Literally in Sanskrit, "prana" means "breath", and "yama" means "restraint" or control.
"Prana" is usually taken to mean a lot more than the standard meaning of "breath" in English. It's more to do with the breath energy, or life energy - the chi. It's also the name of the upward moving energy of the breath.
The A:.A:. texts recommend that one should build up the length of breathing, starting with breathing out for twenty seconds, and breathing in for ten seconds, alternating nostrils.
The Hatha Yoga Pradipika recommends various types of pranayama, varying the positions of the tongue, lips, chin, throat, et al. It seems to emphasise the importance of kumbhaka, that is, the time when there is no inhaling or exhaling. In my practise, I have found that the most energy is obtained during kumbhaka.
I have also heard that the thoughts are fewer during kumbhaka and exhaling. I have found some truth in this.
The breathing should be an important part of anyone's yoga practise, whether they are trying to gain health, magical powers, energy, or union itself.