Prana=breath, life giving force. Pranayama=breath control.
Pranayama is listed after the asanas in the sutras, this suggests that the asanas must prepare us for pranayama.
There are varying pranayama techniques and contraindications as well.
The point of pranayama is to take in vital energy and remove waste products out of our body and mind.
Note: think of how much your breath affects you or how your emotions affect your breath. When you are angry or stressed, don’t you breath faster? This is why taking a deep breath in high stress or tense moments is often recommended.