DRM stands for Digital Rights Management. It's basically a method of preventing piracy, that comes with a lot of PC games these days. An example of basic DRM is for a game to require the disc to be in the computer to run.
Some DRM isn't bad, like the just-mentioned simple disc check, but others are much more elaborate, and the common opinion is that they hurt the honest consumer just as much as (if not moreso) than any pirate. A notorious example of DRM came with Assassin's Creed 2, requiring you to be online constantly to play, even though it was a singleplayer game with no online content whatsoever. Another example of bad DRM came with Bioshock, and only let you install the game a few times before locking you out entirely.
So to get back to your question, the term "DRM free" means that the product has no DRM whatsoever. They are giving it to you as is, and if you so choose you can then proceed to do whatever you want with it, i.e. upload it for others to play for free, give it to your friends, etc.
It's basically a gesture of goodwill and trust. They put faith in the belief that you will not cheat them, and in return you get to play the game completely unhindered.