I think the biggest things are the gameplay opportunities afforded by a controller (admittedly possible via PC as well), potential for split-screen games, and easy setup. Try playing 4-player Mario Kart or Super Smash Bros. (or any fighting game, for that matter) on a PC. Sure, you could have a player per PC, or have players share a keyboard, and go through all the setup and pain (and lag) that results, but why would you, when you can just turn on a box connected to your TV, hand out controllers, and be playing near-instantly, with no lag (for local split-screen/same screen games), and on a screen large enough to make split-screen worthwhile? I'm not much of a console gamer myself, but I recognize that console and PC games have different niches in terms of gameplay.
I agree with that idea conceptually, but other than the fact that it's a console, how does it offer anything different from a desktop/laptop?
Would you ask this same question if we were talking about mobile vs PC?