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Yes you're right. The Apple TV is a small box that connects to your TV and allows you to play anything you've bought in iTunes on your TV. You can also use it to rent movies, watch catch up TV, watch youtube, etc etc. And if you have photos or vids on your phone or ipad you want to show on the TV you can do that too. Personally I LOVE mine and couldnt live without it
It's probably pretty good value for money (something I rarely say about Apple stuff bought brand new) but this > TechRadar review < points out some of the things it won't do, too. (I'm only pointing out slight reservation, because it's not offering full browsing capability, and is locked down by Apple.)