Previous Bungie games Marathon and Myth featured something called demo or film recording, allowing players to record multiplayer matches in small files that could be exchanged with other players.
The UI of the build of Halo 2 shown to journalists apparently had two familiar choices (Campaign, Multiplayer) and a new option, Game Movies. Apparently this might be for recording games or perhaps portions of games. It is rumored to have been cut from the game, however.