Seems you used Debian long time ago, the equivalent of the Windos Store, Gnome Software assuming you are using the default install, doesn't ask for any password...
Well it would be `sudo apt-get install X` and the password is my password. In Windows how do I write a file to C:\ without logging into the administrator account? I didn't know, my friend didn't know, what's happened?
The equivalent of sudo is right click / run as administrator. You can run a command-line shell like cmd or PowerShell, or a file manager this way, and it will allow you to write everywhere.
On the contrast, you can install most apps from Windows Store without admin rights.