Internet Radio is a broad term that refers to music and other audio programming streamed over the Internet.
There are many ways to get the tens of thousands of Internet radio stations. The most basic is to navigate to a channel's website and listen there. The easier way is to use a program like iTunes, which has a section devoted to Internet radio, with stations sorted by category and genre. Many TVs and AV receivers have built-in Internet radio connectivity. There are even products from companies like Logitech that are specifically just for Internet radio surfing.
Audio quality varies greatly, though it is often highly compressed, using a lossy codec similar to MP3.
Two of the more popular Internet radio stations are Pandora and Slacker.
See a preview of Onkyo's new receivers that can stream Internet radio.
Take a look at Yamaha's neoHD streaming media players.