Wave has arrived. The Complete guide to Google Wave does a good job at explaining about what Wave actually is today.
Defining what Wave is, is hard because it means different things to different people. At first it was "e-mail redone with the experience of today", it proved necessary to cut the link to e-mail so that it could become its own thing and for me, I concentrate on Wave as the editing front end to a MediaWiki back end.
The book as it is available today, is the "preview edition", it has its home on a MediaWiki wiki and, it is billed as a work in progress. At that it fits in nicely with the collaborative editing that is the great strength of Wave. Consider, the people that find this important are likely and fall in love with Wave are also the people what are interested in writing the book on Wave. The GoogleWave extension allows for the inclusion of a Wave on a MediaWiki page show Wave to all the people who have not been invited yet.
When you want to learn more about Wave, do read the book, it is well worth it.