New to Iphone 5, I noticed Airplay but have no idea what it is or what to do with it. Seems to have something to do with ring tones or music.
Wireless music. Basically you buy a receiver (a little power plug, a stereo receiver with Airplay, a software program like Airfoil) and then select which speaker you want to beam your iPhone's audio to. For example, if you already have a set of speakers (computer speakers, stereo speakers, etc.), you can plug a small $99 adapter in from Apple to make them wireless:
https://www.apple.com/airport-express/
You can use computers & smartphones as receivers too using software:
https://www.rogueamoeba.com/airfoil/speakers.php
Or get an Apple TV and also do video streaming. I have Airplay on my receiver but it's just hideous looking on the TV so I pretty much always use the Apple TV for the pretty cover art.
Yeah, the only catch is that the AppleTV only has HDMI & Optical Audio outputs, so you need a good receiver that takes a digital audio input to use it for a music player (or a television). Same price though, and converters are available for Coaxial digital audio if needed.