There are two ways to use it:
Enter the Youtube username which the playlist belongs to. In this case only public playlists can be played.
You can give more than one user name separated with commas (e.g. joe,mary) if you want to mix playlists from several users.
If the user name does not work for some reason then use the youtube channel id instead. Here's how to find it.
Alternatively, you can authorize this site to view your Youtube account and then you can see all your playlists instantly, including your private playlists. Click here to do that.