Q: how does airplay work?

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

Apple TV (2nd and 3rd gen)- How to use AirPlay Mirroring

How to set up and configure AirPort Express for AirPlay and iTunes

iTunes- Troubleshooting AirPlay and AirPlay Mirroring

iTunes- Using AirPlay

Apple TV (2nd and 3rd gen)- Understanding AirPlay settings

About AirPlay Mirroring in OS X Mountain Lion

iTunes 10- About playing music with AirPlay

Troubleshooting AirPlay and AirPlay Mirroring

Using AirPlay

Thanks to the $15 Beamer, AirPlay streaming is still possible on Macs  that do not support Airplay and mirroring.

Other solutions are the Air Parrot, StreamToMe, and AirServer.

read: http://support.apple.com/kb/ht4437

https://www.apple.com/airplay/