Taking meeting notes: Instead of one person taking meeting minutes, or everyone in the room taking their own individual notes, a group of people can edit a single wave during a meeting.
Group brainstorming: Likewise, instead of individuals brainstorming ideas separately and then comparing notes, using a single wave gives a group the opportunity to work together and riff on each other's ideas in real-time.
Multimedia chat sessions: Instant messenger doesn't usually allow chatters to include images, maps, and videos right inside their chat, and often there's no chat transcript stored in a single place for later reference, but Wave offers both.