I really liked this article from howstuffworks.com
Breathing is obviously an important part of every day, whether you're doing yoga or not. Though we don't typically focus on our breath during the day, in a yoga class, breathing is just as important as the poses and serves a greater purpose. Each inhale and exhale can energize, calm, and help you form a deeper mind-body connection.
Vinyasa, one of the most common forms of yoga practiced in the United States today, means, in Sanskrit, "breath linked to movement." In these classes, movement from one posture to the next is usually done along with an inhale or an exhale, says Annelise Hagen, a yoga instructor in New York City.
"When you're breathing in, that's when you have more energy -- that's generally when you would initiate a movement that involves engaging or contracting your muscles," she says. "And on the exhale, you typically want to be stretching, lengthening, or relaxing."
In a Vinyasa practice, yogis often use something called an Ujjayi breath. Ujjayi translates to "to become victorious" or "to gain mastery," and using a Ujjayi breath may even help you master your own practice a bit more. To perform Ujjayi breathing, constrict the back of your throat as you breathe in and out through your nose, so that your breath is audible -- similar to a whisper, or to the roar of the ocean.
Concentrating on your Ujjayi breath while you practice can help lead to better focus on the flow from move to move, tune out external distractions and remind you to take full, complete breaths. They key is not to be too loud or too quiet with your breath, but to blend in with the rest of the class.
Some experts also believe that Ujjayi breath generates internal heat and can help regulate healing in the body, as well as relieve headaches, sinus pressure and congestion.