I never played any of the Witcher games. Did some quick Googling and it looks interesting. May have to give it a shot. Is there anything to compare it to? From the videos it looks like it is dynamic in scope, but we all know how trailers can make it seem edgier than it really is.
The Witcher basically started the "no good/evil, just difficult choices" trend in CRPGs, and it does it better than anyone else.
The games are based on a series of books by a Polish author, and the setting definitely has that Eastern European grittiness to it. It's basically standard in that Elves and Dwarves have been around for ages, while Man is a newcomer but has pretty much taken over and the world of magic is being slowly eradicated. Elves and Dwarves are very much second-class citizens, and for the most part live in slums. There's a lot of racial tension, and that's driving much of the conflict in the world. The Elves have formed a resistance group, the Scoia'Tel, that do the kid of stuff you'd expect.
Witchers are people who have been trained and magically mutated through alchemy since childhood to fight monsters. Most don't survive the process, so Witchers are quite rare. They are basically like traveling monks or mercenaries whose only purpose is to deal with monster problems for pay. They aren't supposed to get involve in humanoid politics at all, and Geralt in particular (the person you play), believes in maintaining this separation as his
#1 rule. The mutation process worked unusually well in Geralt's case, and he's probably the most famous Witcher around, dubbed the "White Wolf" because of his white hair.
As you might expect, a lot of the monster problems turn out to be more complicated than just "random creature X is eating babies." Often, it's something a Human has done that's caused the problem in the first place, and given how horrible Humans are in general, it's no surprise that Geralt is somewhat sympathetic to the monster plight. So often you'll find yourself sussing out the truth behind a particular issue and then forced to decide how to resolve this problem where a monster is maybe causing problems but isn't the real cause of the situation. At least if you want to. There's also the option to just roll in, kill the thing, and move on.
At the start of Witcher 1, Geralt shows up with amnesia, after having been missing for months and thought dead. Recovering his memories is a motivating factor for the entire trilogy, and in Witcher 3 you'll see him finally working towards putting all the pieces together. There are a lot of different subplots that make up Witcher 1, and the thing that ends up being the motivator for the big boss battle at the end isn't terribly relevant to the story in Witcher 2 or 3. Most important is that Geralt resolves a problem where a princess has been cursed and turned into a monster, and by solving this problem Geralt wins the favor of a king, who ultimately forces Geralt to be his bodyguard in the interlude between W1 and W2.
W2 begins on a battlefield, with Geralt trapped as this King's bodyguard. Before long, the king is assassinated, and Geralt is accused of the murder. To clear his name, Geralt goes after the real killer, who turns out to be a Witcher (aided by the Scoia'Tel) who has been going around killing kings. As the story goes on, Geralt begins to recover some of his lost memories. Something about The Wild Hunt and a sorceress named Yennefer (who is the love of his life in the books, but their relationship is very tumultuous and so they're basically separated). I haven't actually finished W2 yet (hoping to before W3 is released), but I think the relevant part of the story will mostly be what Geralt learns when he meets the kingslayer he's chasing, who claims to have been Geralt's friend from back in the day. In addition to that, partly because of the kingslaying, there are different kingdoms fighting over land, and the Scoia'Tel are causing their usual problems. At some point you're forced to pick sides (you are in W1 as well, with basically the same factions), and must choose either the Scoia'Tel or the Humans, and both have their good and bad aspects--noble terrorists vs. asshole townies.
As W3 is titled The Wild Hunt, I expect (hope) the main arc will be about Geralt chasing down the Hunt and attempting to rescue Yennefer, who's caught up in it somehow. I suspect that Geralt and Yennefer were together before W1, were caught by the Hunt, and somehow Geralt managed to escape at the expense of his memories.
Geralt also has a sorceress friend named Triss, who is his constant companion in W1, much of W2, and will presumably be around in W3 as well. They adopted a magical kid named Alvin in W1 (the main plot), who may be an analog for a magical girl Geralt finds in the books and hands off to Yennefer for protection. He's also accompanies by a good for nothing Bard named Dandelion, and a Dwarf named Zoltan.