AirPlay is a built-in Apple protocol that allows mirroring of the screen from an Apple computing device to an AirPlay device (i.e. Apple TV or AirServer).
The MacBook is compatible with Apple TV and no physical setup is required. Airplay will detect and mirror from a compatible Apple device to Apple TV without wifi on the newer model Apple TVs (A1469 vs. A1427). However, you can only mirror your screen but it will not mirror video. You will need to connect to a wireless network in order to stream video to your Apple TV.
To use AirPlay, simply click on the AirPlay symbol on the menu bar, and select any AirPlay displays that are available.
Please see Screen Mirroring section for more mirroring options using AirPlay and other means.