At first I wasn't going to post this, out of deference to the bored myriads, but its short and I like it. So here's how the Ramban and the Rav view the Azazel ritual:
Ramban: Both goats are given to God who, by lot, sends one to Azazel the lord of all evil, disease, war and destruction. But this is not a bribe. Rather, its a way to symbolically include Azazel in Yom Kippur. This demonstrates that evil is subservient to God, and that on this day all of the forces in the world are in harmony, the harmony that makes forgiveness possible. The Ramban though Azazel was real demon, but even those of who say demons don't exist can see something wise in this approach.
Rav: How do we have the right to ask God to forgive us? We knew the laws, we made our choices. Justice demands reward or punishment. There's no room for the judge to exercise discretion. The purpose of the Azazel ritual is to remind us that not everything is our fault. Some things are left to chance/things we don't control. Our genes, our environment, the behavior of our friends and our community - all of this works on us, and pushes us in one direction or another. Two twins can live exactly the same lives, but through no fault of their own, one might go to God, and the other to Azazel. It is this (perception of) randomness that makes (the perception of heavenly) mercy possible.
Ok, ad kan Azazel-palooza.
Search for more information about Azazel at 4torah.com.