I've read about a "pancake lens" but don't really understand what that means.
What the pros and cons of having a pancake vs. another type of lens?
I'm thinking of getting a Panasonic Lumix DMC-GF1 which comes with such a lens.
Pancake lens is a lens which is designed to be physically very thin and compact, relatively pocketable when combined with a slim body. Current pancakes have fixed focal length, from moderate wide to moderate telephoto, they're usually relatively slow for a prime lens (f2.8 and slower) although exceptions exist. Pancake lenses don't alter the image in any way.
Although pancake design is quite old, it has been lately popularized by (Micro) Four Thirds system. The currently produced pancake lenses are:
Here is an example of a pancake lens:
"Pancake lens" is a purely physical description.
Actual overall size has nothing to do with it, and it has no implications about image performance, aside from the fact that it's generally very hard to pack a telephoto or fast prime into the pancake form-factor.
It's worth noting that a "Pancake lens" does not have to be small or compact, and a small lens is not automatically a pancake lens. It's only a description of the lens form-factor.