For a while now the YouTube app on both Android and iOS has allowed users to minimize a playing video into a floating window, letting them browse other content without interrupting playback. A similar floating mode is apparently being tested on the web now.
The writers at 9to5Google discovered that YouTube on the web is A/B testing a picture-in-picture feature and it has already started hitting a small number of users. If you are one of the lucky few, you'll be able to start a video and then click anywhere on YouTube (return to the homepage, search, or browse channels) and the video will continue to play in a floating window on the bottom right corner. The name of the video shows up below the window and an icon on the bottom right brings up full scrollable playlists, plus it has play/pause, repeat, and watch next clip controls. However, since this is only showing up on a YouTube Red account, it may be restricted to Red subscribers for now (or forever).
This is an incredibly useful feature that should have been implemented a long time back because it improves the overall user experience. Now you won't need to open new tabs just to browse for other videos to add to your queue. Here's to hoping YouTube rolls this out to everyone and not just for Red subscribers.