Twerking is a dance move involving vigourous buttock motion, generally where the dancer is squatting or bent over. An actual twerker would probably give a more precise definition but that is the gist of it.
As for origination, probably many thousands of years ago, when the first lady shook her rump and decided it was kind of fun. More recently, it is hard to say. Rump shaking is an element of many dance styles all around the world, especially the southern half of the world (Africa and South America) who seem to have a bit more rhythm than we do in the north. An African style called Mapouka or Brazilian Funk are good examples.
In America, the lineage is generally traced to New Orleans Bounce, but I'm not certain if that was a spontaneous creation or borrowed from other places. It is famous now because Miley Cyrus twerked (or attempted to twerk, according to many).