First off, if you're not familiar with White Wolf's Vampire:The Masquerade, this is going to be a lot harder. As a matter of fact, I wouldn't even bother. If you don't already know, I'd suggest you go to some normal web page, where you can read the sports or the tv listings or somesuch. But you don't care what I think, you just want to know what a Malkavian is, and here I've already gone and wasted a full paragraph just babbling on about nothing!
Good, now you're getting the idea.
The first thing you have to know to understand anything about Malkavians is that vampires exist. Really? No, not really, but pretend they do for the moment. Also, vampires are all descended from Cain, who was the first vampire. Yes, Cain who killed Abel and all that. Deal with it. Somehow, Cain became a vampire. Don't ask me how, I don't know. He just did. Eventually, he became lonely, and made three children. Vampire children, made by draining all blood from a mortal, and then giving them some vampiric blood. Don't ask me how he knew how to make children, because I don't know. Anyway, he made three children. One was named Malkav, and he's important, so remember him. The other two you can forget. Malkav, you see, was a bit of a loon. Not quite right in the head, if you get my drift. Anyway, he decided he should make some children, and he did. They were called Malkavians, because the name was just too cool to not have.
Malkavians, by definition, are not quite sane. However, the usual spiel is that through this madness, comes brilliance. And a lot of the time, that's true. Malkavians are famous for knowing things they shouldn't, and also for playing lots of neat little pranks on the other clans, but that's not important, so you can forget that too. The other clans, you say? Oh, yes, them...
The other clans all came from the other two children Caine sired. (Did I tell you they weren't important? Forget that.) The other clans are Brujah, who are rebels, Gangrel, who are animalistic, Nosferatu, who are ugly, Toreador, who are artistic, Tremere, who are vicious blood wizards, and the Ventrue, who are serious. There are others, too, but I don't know as much about them yet. 7;-)
There.
So, in a nutshell, Malkavians are insane vampires. Good enough. And we're lots of fun at parties.