Sorry. I didn't get into too much detail because I've done it so often. Wave is a pretty big idea, so it's reasonable that it might be difficult to grasp what it can be.
I'll try. Keep in mind I'm not known for brevity.
My elevator pitch would be: Wave is a real-time content sharing system. That's the best I can come up with right now, though I think it fairly describes it.
Now, it doesn't sound impressive, but it really is, and better expressed with real world examples. This is easy.
Let's look at this threaded conversation here. If I hadn't come back here looking for any responses, I wouldn't have known you'd respond. I have to come back to /., find my post, and than dig through all the replies.
This entire commenting system can be duplicated inside a Wave. That doesn't mean comments here have to change. Rather, they are linked into Wave. How? The same way email is used currently. However, instead of using an email address, you'd use a wave address.
In fact, anywhere email is used, wave can be used as well.
Now, you're probably wondering if this is the case, why not just use email? The thing is, email only works in one direction. You email me. I email you. Wave works off the premise that communication is bidirectional. So, if /. comments were in Wave, I'd be able to use my Mozilla Thunderfox (My imagined Mozilla Wave client) to see the comments, as well as reply to /. from the client.
Of course, here is where it get's interesting. As I said, I tend to ramble quite a bit, so I'd want to bring in a friend that can better explain this to you. Maybe a bit more concise. Worded nicely, and a lot shorter. He'd do a better job, so I'd share him with the conversation in Thunderfox. He'd be able to see what the conversation is about, and add his own two cents. He'd reply to your comment. He'd also reply to mine, making some mention about how I can't shut up.
He'd also drop in the video of Google showing off Wave, just in case you missed it.
All of this would appear on /. in real time if they wanted.
Being the smart dapper guy I am, I'd steal my friends concise comment, and put it up on my blog (iDontKnowWhenToShutUp.BlogSpot.com). The blog post would let people comment. All 1 of my readers would, probably something like "Honey, don't forget the milk." Everyone subscribed to that Wave (You, my friend, me) would probably be able to see that.
This is all done in real time, on a standard base. Real time communication. Maybe a better way to think of it is IRC meets Email.
This handles a lot of the cases where developers have to create their own APIs to access the inforamtion in a system. If I want to develop an application that posts updates to various social networks, I have to learn a different API for each place. Integrating Wave into these system kinda negates that need for the content sharing side.
I'm not a Wave expert. I'm not going to pretend to know everything. But Wave's goals are big. If they are realized, it will be bigger than email. The problem is, it's so big, so ambitious, it can get rather confusing.
Hopefully I've gotten you thinking. My examples aren't perfect, but I'm sure if you sit back and think for a bit, you could see all the possibilities.