Welcome to the Apple Support Communities
First, open > About this Mac and tell me the Mac OS X version you're running now.
AirPlay Mirroring needs OS X Mountain Lion > http://support.apple.com/kb/HT5404 If your computer is supported, make a backup, open App Store and purchase Mountain Lion. You must be running Snow Leopard (10.6.8) or Lion (10.7.x) to upgrade OS X.
Also, if your Mac isn't supported, use AirParrot > http://www.airparrot.com