Theres a lot of things.
The achievement system (Now its not enough to complete the story, u gotta get your gamerscore up)
Theres also DLC (Now your game is longer than when u first bought it)
Downloadable patches (Imagine what it'll be like if a game's original bugs were permanent)
Downloadable demos and trailers (no more discs from magazines needed)
Multimedia (Nowadays its not just a console)
Firmware (the New Xbox Experience is a great example of what this feature can do)
Wireless (accessories, controllers, u name it)
Themes and gamerpics (makes your console unique)