With the Apple TV in most cases you can watch videos, listen to music, or view photos directly from the ATV using Apple's various services or view content from multiple providers using their ATV apps (like HBO Go or Netflix). AirPlay is not needed.
In some cases the ATV app does not exist (like Amazon Prime Video) so videos or music available via Safari or non-ATV apps which may be playable on your computer or iOS device can be viewed on your TV by using Airplay to send the output of the device to the ATV. It does not work in all cases because of restrictions the content providers may put on using Airplay.
Also there may be cases where you may wish to view your computer or iOS device on a larger screen to share whatever you are doing with others. Airplay mirror allows you to accomplish this.