You need to give more information. What version of InDesign? What computer platform? What are you doing when you're asked for your password? What does this have to do with InDesign?
Usually, that would be the administrator password on your computer, but I can't think of a time I've ever been asked for it when using InDesign.
Another possibility is that the updating software is attempting to access Adobe in which case it is looking for the password for your Adobe ID. This is true if you are using any software associated with an Adobe Creative Cloud subscription.