Prana is a Sanskrit word which means "life force" or, alternately, "breath". Interestingly, several ancient cultures around the world developed this same lexical oddity - the early Greek pneuma, the Hebrew ruah, the Chinese/Japanase chi/ki, and the Polynesian mana all share this dual meaning.
Think of it as the energy that distinguishes a live body from a dead one - something is there in us from birth onwards that keeps the heart beating, the organs functioning, the mind chugging along day after day. That's what the Yogis call prana.
Within the human body, besides being connected with the breath, prana is also concentrated in blood, semen, and menstrual fluid. Prana isn't just found in the human body, though. There is prana in the air, in sunlight, in water, in food - there's prana in just about everything. Even colors and places have particular kinds of prana.
Yoga believes that humans normally absorb and exchange prana through the intake of food and drink, and through exposure to natural elements like sunshine and fresh air.
The word prana actually takes on a few different meanings, depending on the context. For instance, in the Upanishads (ancient texts of esoteric Indian philosophy), sometimes Prana is another name for the Goddess who danced the universe into being.
Prana can actually be sub-divided into different parts when talking about how this general "life energy" gets down to the specifics of bodily functioning and maintenance. Usually when you hear or read someone referring to prana, though, they're talking about this broad understanding of prana as the juice that keeps us going.
If our prana is in good shape, say the Yogis, then our bodies, hearts, and minds will be in good shape too. And just like in the last section, where we talked briefly about the relationship between mental activity and the movement of the breath, in the same way, the state of the body's prana reflects the inner mental state: if the prana is agitated, the mind can't be still, and vice-versa.
That's a pretty important tenet of Hatha Yoga, as the whole approach of this branch of Yoga uses various aspects of the body - breath, energy, and so on - to work on the deeper layers of the mind. That's why prana is such a big deal.
The Big Book of Yoga.