Here's the Starcraft wiki entry on Zerg. http://starcraft.wikia.com/wiki/Zerg It'll have everything more or less in it. In short, the Zerg are an alien race from Zerus. The Xel'Naga found them and altered them to be "pure of essence", which is rather vague but not a lot is said of what that means, but a lot's implied. The Xel'Naga made the Overmind to keep the Zerg from turning on each other as the the Protoss had. The Zerg took over their world, assimilating the other species. Then the Overmind lured some space-faring creatures and assimilated them. From there he used his horde to kill most/all the Xel'Naga. From the Xel'Naga, he learned of their other great project, the Protoss, and decided to assimilate them to become perfect. Then he went. with his swarm to the Protoss, assimilating planets they found on the way. They eventually landed in the Korpulu sector, where the Terrans are.
Oh thanks VampireBob, I thought this was the best place to ask. My friends keep saying to zerg this and zerg that, I had no idea what they were talking about... they were playing Starcraft. What does it mean when you use Zerg as a verb?
Think of it like a blitz in football. Several large guys rush in to squash 1 small guy. Originates from the speed-swarm style of the zerg in general, and the old school 6 zergling rush in particular.