Online gaming store/client/DRM service created by Valve corporation. Games can be bought on Steam, and there are often game sales and bonus pack deals for promotions (Bioshock sold for $10.00 on Boxing Day). There is also a social networking aspect a la Facebook, where you can make friends, join gaming groups, etc.
There are a growing number of games which are using Steam for DRM purposes. These games are, once installed, tied directly to Steam and not your computer. The pro to this is that you can play said game on ANY computer with Steam installed using your account. Games also update themselves automatically. The con is that is that Steam has to be running for the game to play, althought offline mode exists.
The other definitons are outdated and don't represent the improvements Steam has made over the years.
Steam is a great gaming service and the least obnoxious forms of DRM. Yes it is still rather slow but the pros truly outweight the cons. Secu-ROM can burn in hell.
Digital Right Management. The result of an increasing, if not unfounded, fear in a digital age of media piracy and how it could ruin the music and gaming industries. It's basically anything which prevents you, the consumer, from pirating digital content. For example, if you try tampering with your Xbox 360 to play pirated games then the guys down at Microsoft know what you're doing and can shut the console off permanently. Some forms work well and are met with general approval (iTunes, Steam) and others not so much (SecuROM).
Steam and iTunes are examples of DRM done properly. SecuROM is not (see sneaky shit).