Airplay Display, Airplay Mirroring?

Hello!

I am looking to understand Airplay with an apple tv. I want to extend the desktop of my macbook pro to my tv so I can stream video on the tv screen while I use my computer to do homework. After some searching I've found that I'm missing the option in my display. Why is this and how do I get it to extend desktop?

Help!

My Display:

VS One Retrieved from About AirPlay Mirroring in OS X - Apple Support