imagine a WebSite...
that is a simple web app, all alone in the world... remember, you can't add anything else to it, right...?
Now, how about a web project? that it's part of a Solution, and a Solution can have n projects, take my current work for example:
alt text http://www.balexandre.com/temp/2009-06-29_0816_so_question.png
In just one solution, I have more projects than the website, and even if they are in different directories I referenced those projects in the website and it's easy to edit, for example, the ExtensionMethods project when I need to add more.
This is something that you can't control in a WebSite, only in a Web Application Project.
The Web Application Project is like any other project, it includes all files that are in Projects like the proj extension file, and it's treated like a project, for example, you can exclude files to be compiled (you can't in a Website), it is easier to deploy because of the nice plugin called Web Deployment Project", just right click in your WebSite project and choose Add Web Deployment Project...
alt text http://www.balexandre.com/temp/2009-06-29_0825_soanswer.png
And you can deploy only this project (add it to your Web Setup, in order to create the msi file) and you will deploy a compiled website (no source code is showed, all code is compiled into dll's so you can hide the source).
There are numerous advantages to use Web Application Project over a simple Website...