Welcome to the Apple Support Communities
See > http://support.apple.com/kb/HT5404 Your computer is compatible with AirPlay Mirroring, but you have to upgrade to OS X Mountain Lion to get AirPlay Mirroring.
Make a Time Machine backup and/or a clone with Carbon Copy Cloner, open App Store and purchase Mountain Lion. When the download finishes, the installer will appear, so follow the steps to upgrade. To turn on AirPlay Mirroring, select the AirPlay icon in the menu bar or open System Preferences > Displays