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!
How to AirPlay videos from an app right to your Apple TV
Launch the app you'd like to share content from. In my example, I'll use the YouTube app.
Find the video you'd like to share and start playing it.
Tap on the AirPlay icon. The position of it may differ depending on the app you're using. It should always look the same though.
Choose your Apple TV in the popup menu.
Wait for your content to begin streaming.
Whatever you're playing on your iPhone or iPad should now play on your Apple TV instead. To end AirPlay, just follow the same steps again and choose iPhone or iPad to transfer the video stream back to your device.
If the app you're using doesn't have an AirPlay button you can try using the universal AirPlay button in Control Center: