What happens when you click on a YouTube video? Well, it depends. If the video is embedded in a web page and it's already playing, a click on the video will open a new tab and send you to YouTube's page. Until now, this behavior was annoying because the video started to play from the beginning and you had to pause it or pick up from where you left off. Now YouTube's player is smarter: it pauses the video and opens a YouTube page that continues to play the video seamlessly.
You can try the new feature using the video embedded below. You'll notice that YouTube uses a URL format that lets you link to certain sequence from a video:
(where 1m15s is the start time)
Another change is that YouTube's watch page lets you pause videos by just clicking on the player.