How do you use Jenkins libraryResource to read file from resources?

What you're missing is the context/scenario under which usage of libraryResource API becomes applicabLe.

libraryResource: Load a resource file from a shared library Reads a resource from a shared library and returns its content as a plain string.

So if you had provisioned a shared library, then you may use libraryResource inside your shared library to read a resource in located in resource directory of the same shared library.

Hope that clears things up better.