Club sports are between varsity and intramural. Club sports compete against other schools, but don't have the funding varsity sports have. Intramurals are like any other college intramural, you compete within the school. It's company vs company for color points and bragging rights.
Basically, Club sports get enough money for travel, and you pay for everything else, or the other way around. Club sports, at least as of '02 are NOT drill exempt, which if you go to USNA you will learn more about, but for now that means on two days a week when there is parade practice you have to go and either do not practice your sport or have to do so on your own time later. As a club sport you may be competing against a team that is considered varsity at another school, or it may just be a group who is doing this for fun. I had a great time with the 2 club teams I competed with. Most people have some background in the club sport they want to play, but I didn't know what a rugby ball looked like when I went out for that club team. Most of the club athletes played their particular sport in high school and either USNA doesn't have a team or they really aren't at the D-1 level to play it. See the website, and you can get a list of all club teams. Don't see your sport? Find enough people and start a club.
Phantom- still in training, haven't been outside of Texas yet. There are plently of clubs outside of sports, but they don't count for the requirement to play a sport every season.