So what is free-form?
Hunter's got the cut-and-dried definition, ladysharlyne has the more "living, breathing" definition, donsr's 'semi-freeform' is probably close to how many of them actually play out.
tl:dr--think of it as a regular roleplaying game, except instead of rolling dice and referring to tables, the results come from the GM or other players. You still declare your character's actions, attacks, etc, but there's no dice-rolling or other form of mechanics for conflict resolution (or, in the case of the aforementioned 'semi-freeform', the mechanics are extremely minimal.)
The In-depth Version--In my experience, freeform games, moreso than any other style, are heavily reliant on having reliable players with good chemistry. The ones I've played generally involve the players posting what actions their character is undertaking, and possibly even explaining why those actions are being taken ("I throw a rock at the leader," as opposed to, "I throw a rock at the leader to try and knock him over to slow up the rest of his group," for example). The GM then decides what the results of those actions will be (if the group is fighting a bunch of mooks, for instance, the GM may say, "Post your attacks and results, assuming that they all succeed, because these guys are nowhere close to your league," or, referring back to the earlier example, the GM may say, "You hit the leader, but the rock bounces off his helmet without any significant damage. He does, however, appear stunned.")
This is where the 'collaborative creative writing' exercise aspect of it comes into play. If you've ever read anthologies where authors are creating and contributing characters into an established world--Thieves' World comes to mind immediately, although that's a very dated reference at this point--the authors submit their writing and the editor comes back and says either, "That's good, let's keep that," or, "I like this part and this part, but this section right here contradicts what someone else has already written in their story" (or something similar.)
It's reliant on players who are devoted to playing their characters fair and true (which doesn't always happen--you occasionally run into players who are constantly revising their character's background so that no matter what happens, the character has some kind of experience in their past that could be considered applicable to the situation--one of the big knocks commonly heard against freeform gaming), who trust the GM to provide fair and consistent rulings, and also trust the other players to keep their characters true to the setting (like, you don't want someone in a Star Trek game to design an X-Wing fighter, even if the character has the skills to do so, because X-Wings aren't remotely similar to anything in Star Trek).
A good GM can nip most problems in the bud, if they're willing to weigh in on it. Good players can also keep a lid on things (in one of the games I've been in, there was a character who claimed to have been researching the alien race which the PCs were fighting, and claimed that they were genetically modifying each successive generation to be immune to what was killing them now...which is not necessarily a bad premise, but the GM had already established that said aliens, while scientifically superior, were not particularly adept at rapid-fire genetic engineering, and would also inevitably make the aliens invincible, which also flew in the face of the GM's premise for the game. Several of the PCs scoffed at the notion, including statements like, "How do you engineer someone to survive a .50cal to the face?" and the player in question dropped the point in short order.) The big problem that most people complain about is 'god-modding' (or God-Moding), where a player will post something that dictates the actions of or effects upon other characters which they don't control. That is, in most games, a cardinal sin...you're free to have your character say or do whatever, but the ONLY thing you control is your character (unless the GM has allowed you the leeway of having some subordinate NPCs which you also nominally control.)
If you have good players, these problems rarely show up. If you have a good GM, most of the time that these problems show up, they never get a chance to really impact the game. Every so often, you get a player who is just determined that things have got to happen their way, and they are a drain on both the other players and the GM. That said, I've seen similar things happen in system-based games (with rules-lawyering or general Chaotic Stupid behavior).
There's also a strange option called 'freeform sandbox', where the GM literally does almost nothing and it's entirely up to the players to create anything beyond the initial setting. I suppose, with the right people and in the right setting, that could be fun, but the couple of times I tried it, it rapidly started to feel rather pointless, as everyone was busy trying to engineer their own plot-line and nobody was interested in following anyone else's, so after a couple of weeks, nobody was getting anywhere. I'm sure mileage varies on that one, as there are some people out there who rarely play anything that ISN'T a sandbox game...but I prefer a GM providing at least a little general navigation on a game.