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.
Welcome to the Apple Support Communities
See > http://support.apple.com/kb/HT5404 AirPlay Mirroring is only compatible with Mid 2011 or newer iMacs, and OS X Mountain Lion.
If you have a Mid 2011 iMac or newer, you can upgrade to OS X Mountain Lion in order to get AirPlay Mirroring. To upgrade, make a backup of your data, open the App Store and purchase OS X Mountain Lion. When the download finishes, the OS X Mountain Lion installer will appear, so follow the steps to upgrade.
If your iMac isn't supported or you don't want to upgrade to OS X Mountain Lion, you can use a third-party app as AirParrot > http://www.airparrot.com