Capture the Flag is a very popular Halo 2 multiplayer game variant. There are many versions of it found in the game. Traditionally, there are 2 teams; red and blue. Both teams have a base where their flag is kept. The objective is to assault the enemy's base, steal their flag, and bring it back to the home base to score.
Classic CTF is the version of Capture the Flag that was in Halo 1. There are 2 teams and 2 flags, one at each base. There will usually be 4 people to a team. That means that 2 players can be assigned to stay at the base and guard the flag from the enemy, and the other 2 can be sent out to assault the enemy's base.
An team cannot score unless their flag is at their own base. Once a flag is dropped on the battlefield, it can be automatically returned to its home base by being touched by the team it belongs to.