Here's how you can use AirPlay on your iOS device to show videos on your Apple TV.
1. Open the app you want to use to show your video.
2. Start playing the video.
3. Tap the AirPlay icon.
4. Select your Apple TV in the AirPlay menu.
5. Your video will begin streaming on your Apple TV.
AirPlay can be a wonderful way to share videos with family and friends on the much larger screen of your television set.
AirPlay lets you wirelessly beam whatever you're watching on your iPhone or iPad to your Apple TV, even videos in App Store apps like YouTube and Netflix. Any app that's incorporated Apple's AirPlay media button will work. All that's required are a few taps!More at iMore
Additional resources for Apple TV