Bowl I've played has slightly different rule
s than what Metacognizant
describes, but then, I have only played in college.
"College Bowl" is technically the name of an organization (though it's sometimes used as a generic term), one of three major quiz bowl organizations in the U.S., which runs College Bowl tournaments on university campuses, used to run the College Bowl radio and television shows in the U.S. (and licenses their format for the University Challenge shows in Britain) and the Honda Campus All-Star Challenge for historically black colleges and universities.
The standard College Bowl college/university system of tournaments runs like this: each participating university has intramural competition to determine who will be on the team to represent that university at the regional tournament. A team is four students and an alternate, with a limit of one graduate student per team. The regional tournaments have all the participating schools from a few states get together; the winners of the 15 regional competitions and one wild-card team get to go to the national competition. The Honda Campus All-Star Challenge works a bit differently in determining who goes to their national championship, but the play of games is the same.
National Academic Quiz Tournaments (NAQT) and Academic Competition Federation are separate and competing quiz bowl organizations with slightly different sets of rules. College Bowl considers themselves the originators of the college quiz bowl format, but the other two are cheaper to be members of, and many schools send teams to competitions run by several organizations or run their own tournaments in the style of one or more of the major organizations.