What is the WPF browser application type project?

A WPF Browser application is an app that runs in-browser as an XBAP (Xaml Browser Application).

You can find a little more information on the uses and reasons to use XBAPs here.

This thread on MSDN might help also.

XBAP applications (if that is what you are refering to) require the client to have the .NET framework installed (as opposed to Silverlight that only requires the Silverlight plug-in)

This allows XBAP applications to use the entire functionality of the .NET framework which is much broader than Silverlight.