Use AirPlay on your Mac
Show whatever’s on your Mac mini on the big screen using AirPlay screen mirroring. To mirror the Mac mini screen on your TV screen or to use the HDTV as a second display, connect your HDTV to Apple TV and make sure the Apple TV is on the same Wi-Fi network as your Mac mini. You can also play web videos directly on your HDTV without showing what’s on your desktop—handy when you want to play a movie but keep your work private.
In some cases, you can use an AirPlay display even if you’re not on the same Wi-Fi network as Apple TV (called peer-to-peer AirPlay). To use peer-to-peer AirPlay, you need an Apple TV (3rd generation rev A, model A1469 or later) with tvOS 7.0 or later.
Play web videos without showing your desktop. When you find a web video with an AirPlay icon Use AirPlay to stream what’s on your Mac to an HDTV in the macOS User Guide. To learn more about using a second display with your Mac mini, see If AirPlay or screen mirroring isn’t working on your device.