The resolution of YouTube videos can be all over the map. I've seen some that look like bad VHS copies, all the way to high quality 4K video. There's a menu option within the YouTube app called Stats for Nerds, and that gives you all the info about the video you're watching. Without knowing the resolution of the video streamed, we can't make a guess about how it is supposed to look.
And I will say that sometimes the video might be streaming in HD or higher quality, but the video itself (usually something older) is still bad looking.
