Sometimes you may need to debug an application in production. Which means you have to debug the server, somehow.
The best way is to install Visual Studio on the server and attach to the web server process (for IIS) or to the application's process when deployed as a standalone app.
Visual Studio supports remote debugging, allowing you to connect to the production machine with Visual Studio running on your development machine.
Please note that some Azure deployments support Visual Studio remote debugging natively, you just and to enable it.