I believe this question doesn't stray too far from "why do people participate or follow sports."

There is a primal urge to compete and conquer, to excel in a forum of like minded and bodied individuals.
The human race have developed, physically; to a high level, but also mentally to a level that people realise that not everyone can attain elite athleticism. Our mind allows us to appreciate and admire these capabilities.

When you're in an arena, with hundreds or perhaps thousands of people with similar interest in a given contest; you immediately bond with the energies of those on your side and oppose that of the opposition; just as a supporter!
It's all about Feel, Energy and Instinct. Andre's post on this is gonna kick ass.