A wave is equal parts conversation and document. People can communicate and work together with richly formatted text, photos, videos, maps, and more.
A wave is shared. Any participant can reply anywhere in the message, edit the content and add participants at any point in the process. Then playback lets anyone rewind the wave to see who said what and when.
A wave is live. With live transmission as you type, participants on a wave can have faster conversations, see edits and interact with extensions in real-time.
No, that really isn't what a wave is. Silly google.
Yeah, a wave is a transition between a high point and a low point. Or something. Certainly nothing to do with being shared, that just sounds like marketing wankspeak dreampt up by young urbanites drinking wine in a bar and wearing ridiculous haircuts.
Possibly something to do with the flowing nature of the conversations you can have.
There's a link to the demonstration video in the link I posted, it looks very clever.
The best part is real-time language translation that changes words depending on the context in the sentence. Very impressive.
You should try signing up for a dev account if you're creative enough to come up with something you'd like to develop, that way, you'll only have to wait weeks instead of months for confirmation.