“Enable admin account password request” keeps GlassWire more secure by only allowing changes to GlassWire if you have your admin password. Otherwise anyone who has access to your computer could easily change your GlassWire settings any time.
It actually doesnt ask for the Password it just spawns the UAC and asks for admin privileges (well I set my laptop so that UAC forces password but that option is either registry or gpedit, so most users wont even know it exists)
so in short if you are already logged in, by default with this option you get a window asking for the password, but only if you are logged in as a normal user, BUT if you are already are already logged in, you just get a yes or no window.