I think you're initial thought is correct - it's not very well-defined. Indeed, the joke is that REST's primary utility is that it enables you to criticize anything with "but it's not RESTful". Indeed, Roy Fielding himself used to be famous for this.

What REST has come to mean, to me (and perhaps to others), is a URL style whereby data, including application state, is addressed in a hierarchical way. However, I don't think that's what Roy really meant.

The wikipedia article is not bad: https://en.wikipedia.org/wiki/REST