So, How's This Work Exactly?

This is my first experience with the NCAA tournament, or, what adults refer to as "March Madness." I don't necessarily get what is going on exactly, but there is one question that I have: Why did Arizona make the tournament and Arizona State did not?

For example, Arizona finished 8-10 in the Pac-10 and 19-14 overall. ASU went 9-9 in the league and 19-12 overall. Soooooo, ASU had a better conference record, a better overall record, and beat Arizona twice. Hmmm. Let's look deeper. Arizona lost to Stanford twice, UCLA twice, lost to Oregon twice, and split with Washington State. ASU? Split with Stanford, lost to UCLA twice, split with Oregon, and lost to Washington State twice. They also beat Xavier and split with USC, as did Arizona. What teams that you may have heard of  did Arizona beat that weren't in the Pac-10 and that are as good as Xavier...

Oh wait, Arizona beat Adams State. That might have been the difference maker.