About AirPlay and Airplay Mirroring
AirPlay Mirroring requires a second-generation Apple TV or later, and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer). For non-qualifying Macs you can try using Air Parrot.
Several Apple Articles Regarding AirPlay
Thanks to the $15 Beamer, AirPlay streaming is still possible on Macs that do not support Airplay and mirroring.
Another solution is the Air Parrot.
You are running OS X Lion and AirPlay Mirroring needs OS X Mountain Lion. You have two possibilities:
1. Make a backup of your files, open App Store and purchase Mountain Lion. After upgrading to OS X Mountain Lion, you will find the AirPlay icon on the menu bar and on System Preferences > Displays.
2. Purchase AirParrot > http://www.airparrot.com
If you purchased your computer after July 26th, you can upgrade to OS X Mountain Lion for free > http://www.apple.com/osx/uptodate/
As others have mentioned you need to be running Mountain Lion (10.8.x) in order to use airplay:
The apple tv needs to be up to date as well: Apple TV (2nd or 3rd generation) with software update v5.0 or later