While I know that it was useful during manhunts and that Lifehacker loves it, I still don't really understand Google Wave. But no more worrying about this particular lack of knowledge though, because Google appears to be abandoning the project:
Wave has not seen the user adoption we would have liked. We don't plan to continue developing Wave as a standalone product, but we will maintain the site at least through the end of the year and extend the technology for use in other Google projects. The central parts of the code, as well as the protocols that have driven many of Wave's innovations, like drag-and-drop and character-by-character live typing, are already available as open source, so customers and partners can continue the innovation we began. In addition, we will work on tools so that users can easily "liberate" their content from Wave.
Wave has taught us a lot, and we are proud of the team for the ways in which they have pushed the boundaries of computer science. We are excited about what they will develop next as we continue to create innovations with the potential to advance technology and the wider web.