Prana is a term use often in yoga. It has many different subtle meanings depending on who you are talking to however generally speaking Prana refers to breath and the life force that is carried on it. In the eight fold or eight limb path Pranayama is the fourth branch. In this regard Pranayama is used to gain a greater awareness and control over the breath in order to begin the process of bringing stillness and steadiness to the mind.
The Prana body refers to the second layer or Kosha that make up the five layers of being. The Pranamaya Kosha is the energy body. This is one of the layers in which the Hatha yogi works. The energy that flows within this layer of the subtle body is connected to the five different winds or vayus. Because Ashtanga yoga deals with all aspect of the eight limbs equally the Pranamaya Kosha is stimulated every time you breath. The breath is an integral aspect of yoga and so through the practice of asana you will be developing a vibrant prana body.