Gina Trapani former editor-in-chief at Lifehacker has posted an excellent article over at lifehacker (where she still posts from time-to-time) called "Google Wave First Look." I highly recommend reading her post to geek a feel of what Wave can do, that is, if you haven't already watched the demo video from the I/O Conference from earlier this year. Gina also makes this excellent point which everyone who is lucky enough to receive an invite should keep in mind:
Wave is only as useful as the people who are in it, so if you get an invitation and the privilege of giving out invitations, do use them very wisely.
Remember, you only get 8 "nominations" initially. If you blast these out to 8 of your closest friends, 6 of whom are really geeks and might not really use it, you've just run the risk of detrimentally affecting your initial wave experience because you now have no one use Wave with (unless you want to go out on Twitter and find random strangers to try it out with). Be selective with your newfound Wave granting powers :)