Watch this loooong video
http://wave.google.com/help/wave/about.html#video
It's a real-time communication tool. It's more like a real-time wiki than anything else. The invites are to the developer demo, so it may well be a little buggy and not work like the final 'product'. Google has never really done this before, even the GMail 'beta' was essentially the same GMail we use today, and this is exciting because Wave is not just a web product, it's an entirely new and open protocol. I have no idea how they've done this, but they have (seemingly) character-by-character real-time communication. They've released these invites so developers can try to make their own stuff using Wave. Some sort of Twitter wave would be cool.
The current stuff you see in that video looks a lot like e-mail, which I think is a problem because it isn't really e-mail and doesn't work like it. And also, your Wave account is entirely open, so anyone that has your Wave address can send you waves and start talking to you. I think that should probably change, with some sort of privacy settings with Facebook-style friend requests. This is a really ambitious project, and it may well fail because it seems to have a pretty steep learning curve from what I've heard, but if it takes off it could be very exciting.