Originally, it was Apple's first way to get things you bought or stored in iTunes (songs, TV shows and movies) to show on your TV, since previously it was only easy to play and watch them on your computer, or on iPods. Since then, it's evolved to be a receiver to function as a wireless second or mirrored screen for iPhones, iPads and Macs. And a number of actual TV networks have begun to make apps to actually transmit full shows (like PBS, HBO, Hulu and Netflix), and most recently, a full App Store opened up for the new device, allowing developers to write any app they think might be appropriate to use with a TV (such as video games).
Some people no longer subscribe to cable because the AppleTV – sometimes combined with subscriptions to Netflix, et cetera, provides all the TV-ish content they want. In the future, all this will probably continue to expand.