Google Wave is "a personal communication and collaboration tool" - a web-based service and communications protocol designed to merge e-mail, instant messaging, wiki, and social networking.
I got my Google Wave account yesterday (09/30/2009) - it looks like another Knol (a Google Wikipedia clone that few people use) - very much beta - it could be more useful after they activate more features.
If you have a Google Wave account and you send an invitation, they cannot be used immediately - it takes time for the other account to be "activated." Google Wave invites are only nominations and don't necessarily mean you'll be let in immediately http://bit.ly/7IN40
I would set my Google Wave expectations low if I were you - this is probably the best way to be pleasantly surprised when you get your account.
Image source: Wikipedia, Google.
Google Wave's Best Use Cases. Lifehacker.
How to Manage a Group Project in Google Wave. Lifehacker.