Amnesia is actually just one game, though an indirect sequel is coming out on the 10th.
But anyways, you play as a guy named Daniel who (assuming I remember everything correctly) witnessed or heard something so awful he took some sort of medicine to make himself forget, hence the title. It's basically another I-don't-know-who-I-am type of games.
As for the gameplay itself, you have no ways of defending yourself at all. The best thing you can do is sneak, run, and hide. If you get caught, you're pretty much screwed.
Daniel also has an apparent fear of the dark, so if you stand in it for too long your sanity meter slow drains until you go insane and fall over, alerting your presence to all the monsters everywhere. You need to try and use your lantern (which runs out of oil fairly fast, so you must find refills of oil as well) and tinderboxes to light your path. But remember, light makes it easier for you to be spotted.
Honestly I think it's overrated, but the ability to play custom stories created by others makes up for that.