When you connect your device to an AppleTV, the app should show the controls, but the AppleTV should show full screen video with no controls. If you are seeing controls on your AppleTV display, you haven't turned on AirPlay mirroring. This lesson will show you how to connect Projector to an AppleTV and make sure mirroring is enabled.
Note: Only the iPhone4S or later, and the and iPad 2 or later, support AirPlay mirroring. Other devices will need to use a cable.
For information from Apple's Support documentation, click this link here
Swipe Up From the Screen to Open Control Center
Swipe up from outside of the bottom of your screen to bring up Control Center
Choose your Apple TV and make sure Mirroring is ON
You MUST enable Mirroring for the AppleTV to behave as a secondary display. If Mirroring is not enabled, the AppleTV will show you the app interface instead of full-screen video.
If you don't have the option to enable mirroring, either your hardware or software doesn't allow it. To mirror, you need the 2nd generation AppleTV or later, the iPhone 4S or later, and the iPad 2 or later. Check your device for software updates, because sometime if you've updated your iPhone or iPad and not your AppleTV, it can cause problems.
Disable/Enable Second Screen Presentation
If Mirroring is turned ON in AirPlay options and you are still seeing the app interface on your AppleTV, go to Settings and make sure "Second Screen" is Enabled.
Connecting to an Apple TV without Internet
If you have a 3rd Generation Apple TV (Model 1469) or newer, you can use Apple's "Peer-to-peer" functionality to present even without WiFi.
Apple's AirPlay Article States, "Peer-to-peer AirPlay lets visitors to your home or office quickly and easily connect their Mac or iOS device to your Apple TV without gaining passwords and connecting to the Wi-Fi network. Apple TV detects their device and makes the connection. So they can show off photos, share documents, stream movies, or play music right on your TV. Simple as that."
The author of Another Article We Found mentioned that when they tried Peer-to-peer Airplay out, streaming was near perfect, and they attributed it to the fact that they had one less device in the chain of connection - the router.