For class library, we have DLL after we successfully compile the project. And probably you will not feel Xap file is new if you working in Silverlight project.

This link is cool and super clear to explain what is XAP.
Here are some really important FAQ to me about xap:
What does XAP mean?
XAP (pronounced ZAP) is the file extension for a Silverlight-based application package (.xap). This file contains the compressed assemblies and resources of a Silverlight 2 application.

What is a .xap file?
A .xap file is a Silverlight-based application package (.xap) that is generated when the Silverlight project is built.

How can I view the contents of a .xap file?
To view the contents of a .xap file you can rename the extension of the .xap file to .zip. Then view the .zip file using any standard .zip utility.

What are the files contained in the .xap file?
A basic xap file will have an assembly related to specific code for the application, an application manifest file and any additional assemblies need to run the application. At a minimum, two files are needed, the application manifest file and the application assembly.
For example:

What is contained in the AppManifest.xaml file?
The AppManifest.xaml file contains the deployment details needed to run the application.