In high school sports they have Freshman, Jr Varsity and Varsity programs. Usually the athlete will start out - especially as a freshman - on wither the Freshman team or the Jr Varsity team. Varsity is the highest level team in high school sports.
Many sports, usually team sports, you get assigned to Freshie, JV, or Varsity at the beginning of the season and stick with that through the whole season. This is very imporant because teams need to practice together as a team and such.
In other individual sports like gymn or track, you can often move up and down depending on your ability and other circumstances. For example, someone who runs track and is eligible for both JV and Varsity could move up to Varsity on a meet by meet basis depending on their qualifying times and such. But there are limits to this, since like you can't have a senior on the freshman team for example. And in sports with different events where they often want the "best 4", "best 5" people, etc., then you can compete varsity in some events and JV in others, much like FlipTwistFly is doing.