Breath is the threshold. It is the threshold between man and nature, the bridge between body and mind. Breath is the thing in us that most closely mirrors the nervous system: it catches or accelerates, is restricted or inhibited, it seethes or settles. It is one of the few things in the body and in life that can be both: voluntary and involuntary.
Therefore, if we want access to awareness, attention, underlying states of mood and character, breath is the door.
Yoga teachers tend to talk about breath a lot, but rarely teach it. I don't care what postures you can do - if it isn't related to the breath I'm not sure it's yoga.