Enabling password free software installation with parental controls on to block adult content
The password window shows up when an app needs administrator access to access certain files or folders not in the user's home directory.

You may be able to bypass this, depending on how the application is distributed.


If the application is distributed by itself or in an archive(such as a .dmg or .zip) that just contains the app with no installer, you can drag-and-drop the application to the user's Applications folder(/Users/[your username]/Applications/) instead of the system Applications folder(/Applications/). If the user's Applications folder doesn't exist, you can create it yourself.
If the application is distributed as .pkg installer, it may provide the option for you during installation to "Install for me only" which will not require an administrator password.