YouTube is reportedly testing out a new Smart Downloads feature, which downloads 20 videos each week based on your watching preferences. Of course, the app will download the content only using Wi-Fi. The mission is to save up mobile data when you are on the run and watching your favorite channels.
The new feature can be accessed only by Premium subscribers in Europe. You can enable it through Settings > Try new features > Try it out. You should do so before February 14 to participate in the testing stage.
The app will always notify you if you are running out of storage before downloading any videos and you can see the downloaded videos in your Library tab with the rest of your downloaded videos.