Like Pat said, it allows profiles to be glued in that couldn't be with just two pieces. It actually makes a rather big difference in that regard and worth the few additional minutes it takes to grind another lam. More lams seem to hold their glued in shape better too in more highly stressed designs. I've used them to make some pretty intense d/r and d/recurve bows.
The center lam can be a lighter weight material, or 'lesser bow wood' and still make a top quality bow, since it mostly just takes up space and doesn't have to be exceptional in compression or tension resistance properties, which may aid in performance.
A third lam also makes any minor or moderate imperfections in any of them less sinister, especially if in the center.
Yeah, they can look cool, but I often cut the center and belly lam from the same piece of wood, or dye the bow, and so the finished product makes it almost impossible to see that it actually is a trilam... still worth doing