Because literally with the press of a button you can make the video playing on your iPhone or iPad appear on your HDTV.
Because you just plug in the Apple TV and hook it to your wireless network and it shows up on your iOS devices instantly as a recipient for video and music streaming.
No setup. No confusing configuration. It just works.
It's the same reason that Apple was the first company to really get video calls to work. Other vendors and phone companies tried to get video calls to work...and some of the tech crowd certainly made use of it. But Facetime was the first video calling system that made it ridiculously easy for non-technical folks to use.