YouTube has a new feature, a mini player. This is a picture-in-picture mode, which allows videos to continue to be while the rest of the site explores. So you go with it.
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The mini player is hidden behind a new icon next to the settings button, second from the left. See the image at the top of this article. As soon as you click it, it moves the video in a separate window to the bottom right of the picture. You can now to other videos on YouTube search while the current movie continues to play.
Much more is not there. But if the video is part of a larger playlist, it is also to see which songs in the queue. Click at the bottom on the arrow icon that points down. The whole playlist is then displayed, as shown below.