The previously-announced replay videos aren't "videos," per se, but stored data of every action in a match, which therefore creates a smaller file that can be replayed in high-quality (and hopefully allow for a free-roaming camera). Replays can be cut down to specific moments, exchanged with friends, and watched as a group. You can also capture your own screenshots and trade those as well.
Replays, screenshots and even custom game preferences can be transferred between players via a file share option that comes up by clicking on a player's gamertag. As IGN put it, "easy." Judging by the images, Halo 3's graphics are looking better than the beta. The game is due out September 25.