Show whatever’s on your iMac on the big screen using AirPlay Mirroring. To mirror the iMac 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 iMac. 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.
Apple TV is sold separately at Use an external display with your iMac.