Technically, it means "liver-cheese". But it's not liver. And it's definitely not cheese. The best way I can describe it is as a hot dog baked in loaf form. It tastes very similar to a hot dog, and has pretty much the same consistency, and is probably made up of all the same mysterious animal parts and fillers, but for whatever reason, Germans prefer to eat a big slab of it rather than a long cylinder. Maybe the thought is that it would then somehow become confused with all the other myriad types of sausages on offer in Germany, and that just cannot be.
So I actually recommend trying Leberkäse while in Germany. I'm kind of a big fan. Particularly when you run across some of the spiced versions which are not normally on offer. Pizza spice is my favorite (I know. I know. I'm almost ashamed of myself. Except, well, I'm not). If you don't see a spiced version, I usually just eat plain Leberkäse with a smear of sweet mustard on a Semmel (the round, white buns that are ubiquitous in Southern Germany). That's the most common way to enjoy it, and you can find Leberkässemmel at pretty much any butcher, grocery store, gas station, or convenience store in the entire state of Bavaria. Oh yeah- and it's a really cheap meal. Usually less than 2 Euros. So go get one.
*My excuse is that I just got home from vacation and there is really nothing to eat in my refrigerator. Okay? Yeah, totally justified... right?