One word: Matchmaking.
This simple yet effective multiplayer mechanic flat out changed the face of console online multiplayer (which, relatively speaking, was still in its infancy, with Playstation 2 lacking a console-wide service, and Xbox Live being only two years old).
Prior to Halo 2, finding a match online went something like this: 1) search for a gametype; 2) find a player hosting a room playing that gametype; 3) join the room; 4) wait for enough other players to also join the room in order to fill the game quota; 5) hope to have a good time with players who may be of a completely different skill level than yourself (higher or lower); and 6) play for as long as the room host wanted to play, and/or wished to remain on that gametype. (Also, hope that everyone's not a complete douchebag.)
While the douchebaggery remained in place, and would have to wait for Halo 3's ability to easily mute the other team (I once broke a cell phone unintentionally over frustration with some a-hole's taunting), Bungie changed everything else about the online experience.
With Halo 2, you selected your gametype, and the game would find other players who also wished to play that same gametype. It would then automatically set up a room, map, and level settings with the appropriate customization to match the desired gametype. (Halo 3 and Halo: Reach would subsequently add the ability to vote on and veto gametypes, responding to criticism that matchmaking allowed for not enough specificity in player input.)
At the end of the match, you would then continue on to the next game, being paired once more in the same fashion with random players who also fancied the same gametype.
With this new system, you were no longer at the mercy of (pardon the phrasing) finding a human host, or hosting a game yourself. The engine took care of all that for you, allowing for less uncertainty in gaming sessions. Furthermore, ranked ladders assigned you a number based on your skill level, helping to ensure that you would, more often than not, be playing in a competitive match.
AND if that all wasn't enough, Halo 2 introduced the "party" system. allowing one player to "host" a group of fellow gamers, and have them automatically follow him or her, be it to a matchmaking set or to a private custom game. This was unheard of, as all other online titles required players to travel from lobby to lobby solely on their own.
For whatever its faults in single-player content (the cliffhanger ending was widely derided as being anti-climactic and too sudden), the foundation for today's streamlined online experiences with PS3 and Xbox 360 was laid by Master Chief's sophomore outing. It's a pity that the original Xbox Live server no longer exists (which didn't stop a group of stubborn gamers who refused to leave upon the server's shutdown). But, the gameplay lives on in Halo: Reach, and the path blazed by Bungie has since been expanded upon by other FPS mega-blockbusters like the Call of Duty and Battlefield franchises.