Here’s a few excerpts from their FAQ, they do a better job of explaining it than I can.

What is Spotify?
Spotify offers you legal and free access to a huge library of music. All you need to do is create an account and download our streaming music player.
What is your goal?
Our dream is to let everyone listen to whatever they want, whenever and wherever they want.
Do I need to pay to use Spotify?
No, the advertising-funded version of Spotify is free of charge, however, for now it requires that you receive an invite to register. Alternatively, you can pay for an ad-free subscription to Spotify.

I’ve been listening for quite a while now and I’ve only heard one short advert so far, so it’s totally acceptable in that respect unless you really hate ads. I’ve got a feeling ads will get more frequent as their user base grows but for now it’s great.

It’s only officially available for Windows and Mac at the moment but apparently it works under Wine on Linux.

Here’s a screenshot from their site:

Spotify