YouTube adds cool visualization for browsing related videos
In order to access the feature, first full-screen your chosen video. At the bottom left corner, next to the play/pause button, you should find the the new button. Click on it, and YouTube will take you on a cool, new related-video ride.
In testing the feature, we discovered that not all videos had the button. Further investigation led to the culprit: Videos that YouTube considers promoted content (YouTube is likely paid to promote these videos) don't have it. If for some reason a video or two doesn't have the button, fear not. Google has a habit of releasing gradual updates to its properties, so it shouldn't be too long until it becomes a site-wide feature for all videos.