It is often desired to have a final version of the project on the production server for testing purposes, but so that nobody other than site administrators could see things. Also, once in a while, one needs to have a “Site under maintenance” page, even if for just a little while.
There are, of course, many ways to achieve the desired effect (e.g.: using a custom theme or an index.html preceding index.php). But probably the easiest and the most “proper” is by using Maintenance Mode Plugin. It provides a number of options to customize the displayed message, as well give visitors a hint of when it is better to come back. But what is more important, it allows logged in Administrators to see and use the web site like usual – invaluable for testing, as well demonstrations of a ready project to the client.