iTunes in the Cloud allows you to stream a lot of your purchased content right to any Apple TV in just a few button presses. This includes any tv shows, movies, or music that you purchase. That means there's no need to burn anything to a disc or AirPlay from an iOS device, as long as you've got an Apple TV.
How to stream movies and tv shows to your Apple TV with iTunes in the Cloud
From the main menu of your Apple TV, click on Movies or TV Shows.
In the top navigation, click on Purchases.
That's it, just select the movie or TV show you'd like to watch and play it.
How to stream music to your Apple TV with iTunes in the Cloud
From the main menu of your Apple TV, click on Music.
In the top navigation, click on My Music.
Navigate through your music collection and play whatever you'd like.
It's worth noting that some movies and TV shows may not be eligible for streaming. This is typically due to licensing agreements between Apple and whoever released the content. Sometimes movies that weren't previously available for streaming may simply show up one day. Unfortunately, the opposite can happen as well, though it rarely does. Does being able to easily stream movies make you prefer iTunes for your purchases over other methods? Let me know!