Google has added a feature to YouTube that lets users start a Google+ Hangout from any video page. You could already watch YouTube videos in hangouts, but this is probably a better way, because it may inspire you to share the video as you come across it.
There was no real announcement from Google about the feature, but Google's Rick Klau said in a Google+ post, "Fun to see new features get discovered." He then pointed to a link to a blog post from Brian Krassenstein at Google Plus Headlines, where he points out the feature.
When you click the "share button" on a video page on YouTube, you are presented with various sharing options. This one appears in the same area, yet a little separate from the other ones, presumably to make it stand out.
If you're still unfamiliar with Google+ (it is still in invitation-only mode, though invitations are getting easier to come by), Hangouts is a feature that lets you group video chat, and watch videos together if you like:
Hangouts has been one of the more hyped features of the service. Watching YouTube videos with friends seems almost like what the feature was made for, so this new feature makes tons of sense. Of course, Hangouts can serve other purposes like business meetings, online family reunions, etc. Google itself has been using it to talk to users to get ideas for new Google+ features.