Airplay mirroring does not work, i can sellect apple tv but i cannot select mirroring, it does not show the option mirroring, button airplay i can select

If you are sending content to your ATV then that is utilizing airplay and you need to clarify what is happening. Airplay is done within an app (if compatible) and mirroring requires a double tap of the home button, swipe from left to right, select ATV and toggle ON mirroring. What firmware is currently on your ATV, have you tried a reboot or reset on it?

Okay...I think I'm greeting closer to understanding. I appreciate your patience.

I do see a new icon in iTunes that allows me to send things to the appletv. I can send YouTube video as well.

I think, therefore, AirPlay is working.

What I don't see or know about is mirroring.

If I double tap the home button all that happens is I get the option of showing what apps are currently running. Swiping after this does nothing for me.

No problem. Which way are you swiping? It should be in a left to right motion, this will also bring up the volume and brightness controls

Be sure to run the software update on your apple tv. I had the same issue with a fresh out of the box device. Ran the update and everything worked fine

Will Airplay mirroring work from a mid 2010 Macbook Pro to Apple TV?

No

http://www.apple.com/ca/osx/specs/