What's the XML file that comes together with a .NET assembly file?

It is the code comments / IntelliSense file, and is used by the IDE (i.e. Visual Studio), not the runtime - it is where all the extended method / parameter / type descriptions etc come from.

You do not need to deploy it with your binary, but it does no harm either. It is also entirely optional in the IDE - just: IntelliSense will be less informative to you without it (it will just display the names and types, etc - not the more verbose method descriptions).

In your own library, use the /// syntax to write your own code comments, and enable the XML file generation in project-properties.

This is the XML documentation for that assembly. This is only used for Intellisense in VisualStudio. Refer this answer for details.