Pranayama is the part of yoga deals with breathing exercises to let us take control over the Prana (vital life-force). While Prana can be understood as the source and cause of movement in our breathing.
There are various types of Pranayama. The whole concept of Pranayama is based on the link between breath and mind. Breath is said to the vehicle of mind, when the breath is slow and deep, the mind happens in its calm state.