When this box is checked in the Settings tab of your app, you can define a username and password that restricts access to your app in run-mode. (Please note that the concept of username and password is completely different and separate from the concept of a user in the app.)
If you only want to apply the password protection to the Development version of your application but not the Live version, you can check the box that states "Do not apply password for Live," which can be found under the Username and Password inputs.