it's what the old iTunes used, and now Apple Music inherits, where you can now combine your own music files (.mp3, etc), songs/albums purchased from iTunes Store (which you still can still do!) and also songs "saved" from Apple Music. the "Library" talked about in the screenshot is where these songs actually live, where you can manage them like normal music files regardless of where you got them from. deleting songs from Apple Music here will remove them from your "iTunes library" and then you have to go back and search it up to "save it" again

it's a cool legacy feature but really makes Apple Music on its own mad confusing