When I deployed my first, newly created SharePoint app, I was repeatedly being prompted for the authentication.

As it turned out, it was due to the loopback checking, which is a feature of the Windows Server. More details can be found here, http://www.dynamics101.com/2013/06/sharepoint-loopback-checking/

This feature can only be disabled from the Windows registry.  To do that, run the following command in the PowerShell, launched with the admin privilege

New-ItemProperty HKLM:\System\CurrentControlSet\Control\Lsa -Name "DisableLoopbackCheck" -Value "1" -PropertyType dword

Key Takeaway

As has been mentioned in the link shared above, this action should only be performed on the dev environment that too, when you’re in full control of your system.