UKking

Well, Valve in particular uses Valve Anti-Cheat in its games to prevent it, and there are other systems that prevent it such as PunkBuster. You're quite right that there's no way to stop people from modifying the game on their PCs, however, there are ways to tell if someone has done that to give themselves an unfair advantage online. It's not foolproof, but VAC in particular has been very effective, partly because it's adept at detecting cheaters, and partly because if a game needs activation on Steam (Valve's gaming service), as Counter-Strike does for instance, then the threat of being banned from playing is often enough to stop players from trying to cheat. In Steam's early days, Valve were very aggressive in banning cheaters and people who were illegally downloading games, and earned a lot of hatred this way - however, that policy seems to have paid off because people quickly realised that Valve's ruthless approach to cheating and piracy wasn't worth trying to fight (plus the fact that Valve's own games, Half-Life 2 and Counter-Strike Source, needed Steam to run, and the popularity of those games essentially ensured that Steam was here to stay).

Anyway, the talk of Steam and prevention-before-the-cure is getting off the point somewhat.

Basically, here's what happens: The server does no processing in terms of game content; all it does is provide the common hub for game data to be exchanged between players. The player's PC has a copy of the game which is verified by whichever anti-cheat system is being used, and what that means is that the server believes that your version contains the same code as everyone else's. So gravity is the same for you, the number of bullets to a gun is the same, the guns' power is the same, you don't have noclip enabled or anything like that... the playing field is level. These things are regulated by the server - that is to say, everyone's game has to match up with what the server will accept; not only this but the server admins can change the rules in-game, and often these are put to the vote, so you might to say whether you want the change the map, or whether you want low gravity, or a knives-only round, or any number of other changes.

If a server doesn't use an anti-cheat system then, AFAIK, there's nothing to stop you from doing what you like. Unless the other players get pissed off with you doing so well and have you banned. Most players are honest, and they'll get very annoyed very quickly with cheaters.

The main advantage for getting the server to process game content is that it would really put paid to cheating online. But it would add so much work to the servers - and probably do some damage to your ping - that the trade-off would make it worthless. Your computer processes that stuff because, well, that's what it's there for - that's why you'll be able to run higher resolutions or put more effects on when you upgrade.