A Resource is an object which responds to some subset of GET, PUT, POST and DELETE. It has a unique URL which identifies it.
(OK it's a bit more complicated than that, but you get the gist).
At present Controllers in Rails are a flat grab-bag of procedural code loosely associated with some group of resources, with meta-programming used to sweep some of the mess under the carpet. They're not an elegant way to model RESTful concepts.
(I actually have a framework in development for doing resource-oriented APIs on top of Rack, however it's currently very pre-1.0)