Use AirPlay to mirror the screen from the Mac to the Apple TV
From the iPhone screen to the Apple TV, you can demonstrate on a large screen. AirPlay can also help you with screen mirroring if you want to stream something from your Mac to Apple TV.
You will need:
Apple TV with the latest Apple TV software (2nd generation or later)
Mac computers with OS X Mountain Lion v10.8 or later, as shown below:
iMac (mid-2011 or later)
Mac mini (mid-2011 or later)
MacBook (early 2015 or later)
MacBook Air (mid-2011 or later)
MacBook Pro (early 2011 or later)
Mac Pro (Late 2013 or later)
Steps for mirroring a Mac to an Apple TV
Step 1: Enable the same Wi-Fi
Make sure the Mac and Apple TV are on the same network.
Step 2: Open AirPlay
Click the AirPlay status icon in the menu bar, then select your Apple TV.
Step 3: Mirror the Mac screen
To set whether your desktop matches the size of your Mac screen or TV screen, click the AirPlay status icon, then select “This Mac or Apple TV.” When using AirPlay mirroring, the AirPlay status icon in the menu bar is blue.
On your iPhone or iPod touch, tap to find a list of available AirPlay devices, then select the Apple TV you want AirPlay to.