Not the easiest thing to search for.
I stumbled on the "Share" feature while messing around with the new UI.
I did find this.
URL shorteners were thought to have lived their heyday earlier this year when every other startup was in the link shortening business. After a while though, it became clear that there was simply no space for all of them and with Bit.ly the unchallenged leader in the market things looked settled. Last week though, things changed dramatically as both Google and Facebook entered onto the scene with their own take on URL shorteners. And it's not over yet, YouTube has also come up with its own shortener, and this one too is slightly different than the others.
“It's all the rage: link shorteners to ensure that those useful URLs you're sharing don't take up too much precious character count while also giving you an inkling of what you're about to click on. Well, we've just launched youtu.be as a shortener for YouTube video links -- and nothing but YouTube links -- so you can rest assured that when you see a link with this URL, you are indeed about to click on a YouTube video,” Vijay Karunamurthy, engineering manager at YouTube wrote.
YouTube made some interesting choices when implementing its own shortener compromising length for usefulness. The new shortened URLs aren't exactly that short, certainly not compared to the standard Bit.ly not to mention J.mp. Apart from the custom address it uses, youtu.be, which could have been at least a couple of characters shorter, what comes after could have also been shorter.
The dev team decided though to use the existing unique video ID of the clip as part of the shortened link. So, instead of the normal URL which looks like this
http://www.youtube.com/watch?v=cebbvcMW5Uo, you get something like this youtu.be/cebbvcMW5Uo. This approach has the advantage that, because the video ID is in the link, third-party developers can use it for things like thumbnails or even embed it inline. You can use the AutoShare function, which shares the videos you upload or watch to Twitter, Facebook and the likes, to see the shortened links in action. Another option is to create the link manually by adding the video ID to the end of 'youtu.be/'.