Basically, the 30 or so conference champions (from the Big East, PAC-10, ACC down to the smaller conferences) plus 30 plus at-large teams play in a 64-team single elimination tournament for the college basketball national championship. More recently, they've added additional teams...now there are 68 teams and 4 early games/play-in games.
The tournament takes 3 weeks, with each team playing 2 games a week until they are eliminated. Some of the later rounds have names like the Sweet-16, Great-8, Final Four etc.