google wave is basically a cross between forums/e-mail/ and chat
basically its like e-mail because you can sort through conversations as if they were mail
its like a forum because you can have ongoing coversations on organized subjects in a public manner
and its like chat because you can do it in real time
basically its like having a saved aim/msn conversation, but you can keep it in your mailbox, and you can add to it in real time, and so can anyone else who was in the conversation.
also it has a crapload of other cool features. One of the key benefits to the way it is set-up is the collaborative aspects. Like for instance I want to write a screeplay with one of my buddies, so if we wanted to we could bounce back dialog as if we were characters in an improve and save different plot points as chapters or story arcs. We can sort of do this in a regular chat client, but only one of us would have access to the conversation in the end, or if we both saved it we would have to combine them together later.