Not all brains are bumpy, actually. Rats, mice, birds, and many other animals have fairly smooth brains. And it's only the outer sheet of the brain, called the cortex, that we're talking about. Other parts of the brain, ones hidden beneath the cortex, have many different shapes.

So why is the cortex folded in some animals but not others? It has to do with something called surface area. The cortex is a sheet - picture a rectangular blanket. In some animals, like humans, this sheet is large relative to the other parts of the brain, so the only ways to pack it all into a skull are to (a) find a bigger skull or (b) fold it up. Ours got folded up, hence the bumps and grooves.