Maybe I just don't understand how it works, but I never saw the point of it.
It was like the combination of Instant messaging with a forum with email. It was collaborative like a wiki too so with the right permissions you could edit other peoples posts too.
If you've ever had to deal with emails at work where multiple people are copied in and adding their comments and it becomes a massive mess of RE: RE: RE: RE: etc the usefulness is obvious.
Teatimes issue is a good example of where it would have been useful.
It probably never really took off because (afaik) they didn't release the code for corporations to set up their own systems. The strength of Wave was when dealing with small groups of contributors on a specific issue, Most of the public waves had hundreds or thousands of contributors who diddn't follow guidelines on how to post which ended up spawning massive threads that bogged down most systems and were difficult to follow, which turned people off them.
I had some success using it to keep in contact with family members, our family wave was kinda like a private facebook for chatting and sharing photos etc.