From the Store description:
File Downloader is an excellent app to download single or multiple files from YouTube, websites and FTP sites. Password protected sites are supported and files are downloaded in the background.
Some screens of File Downloader UWP in action, on my Lumia 950:
Tappable 'readme' panes do a good job of explaining the main download formats and features - nicely done.
Although you can 'share' to File Downloader, it's just as easy to copy a URL from Edge, as here, and you'll find that it auto-pastes into the Download field, ready for you to tap the 'Download' control.
And there we are, Hazel O'Connor, downloaded to the specified (in Settings) folder and playing in Windows 10 Mobile's built-in video player!
As I said, I tried other video sites with mixed results. More trials needed, so go download the app! (right) the hamburger menu and, at the top, a toast confirming one of the previous downloads has completed.
In the extensive Settings, a choice of themes, plus whether to have each download completion notify you; (right) you can set the YouTube resolution you prefer - 1080p and above aren't available via any 'ripper', by the way, for DRM reasons. If you select 720p and only a lower resolution is available, perhaps because it's an older video, then that will come down instead.
As mentioned in the description, you can do an awful lot with this tool in terms of other big downloads, should you want to try them on the phone. Or, this being a UWP app, maybe it could be part of your main Windows 10 desktop workflow?
You can grab File Downloader UWP here in the Store. In theory, there are adverts and a small IAP to remove these, but I haven't seen any yet!