The description is this:
Opera Unite is a unique technology that turns any computer or device running Opera into a Web server. In other words, your computer (running Opera Unite) is truly part of the fabric of the Web, rather than just interacting with it, and it’s something anyone can use.
Doesn't really say what it really is though. Basically the idea is fairly simple, code in the browser runs a small server, which then uses technologies like uPnP and DNS CNAME records to allow users at large to get right to your browser. So if you enable the 'music player' application the browser runs a little webserver that lists music on the computer (in a directory you point it to) and then points <yourusername>.operaunite.com/music to your routers external IP. Combine this with password protection and you can now listen to your music from work. Fairly simple, still fairly revolutionary.
Guess we'll see if it catches on (and if Opera's past has shown, this means "this feature will appear in Firefox 5.0 and IE 11 :)
Some more good analysis over here. Pay attention to the pictures illustrating how things all fit together.