Yoga is at the root, a practice of meditation to reach a higher level of consciousness. Steadying the breath and keeping awareness on the breath calms the mind. During a vinyasa flow practice, the deep inhales through the nose brings in oxygen and prana (life force), every exhale through the nose removes carbon dioxide and toxins.
Breath is the most important aspect of yoga to engage during any practice. There is no movement without breath. Continued awareness to the breath during a vinyasa flow leads to a connection of the mind and the body. Continued awareness to the inhalations and exhalations can create a meditative like state and will lead to a loving meditation.
During a vinyasa flow practice, the breath used is called Ujjayi. To do this correctly, inhale and exhale through the nose with the back of the throat and the vocal diaphragm contracted. Now your inhales and exhales will sound something like Darth Vader. Keep the inhales and exhales at an equal length and allowing space between the breaths.
Try the Ujjayi breath now for 10 inhales and exhales of a minimum of 3 seconds each. See what you feel during and after the breaths. Work on quieting the mind at the same time.