The best way to understand it is to read Roy T. Fielding's dissertation on it, or relevant articles on his blog where he discusses the differences between pure REST and simply RPC architectures.
Another thing to note is that the Wikipedia article on REST is in dismal condition and Fielding himself, the 'inventor' of REST, suggests that the article is inaccurate.
The biggest thing people miss with REST is discoverability - resources should include URIs for other related resources inside their hypertext, instead of relying on URI naming conventions, which are out-of-band and non-standardized.
A big problem with popular RPC implementations like SOAP or XML-RPC is that they use HTTP underneath their own proprietary architecture, rather than taking advantage of all the different properties of HTTP like PUT, GET, DELETE etc. So this doesn't fit the traditional web stack as well - a cache server in the middle doesn't work, for example, without knowing about the meaning of the contents of the RPC call.
This is an incomplete introduction to REST and RPC but I think I've highlighted some of the important points that are often missed. Be careful, since there is a LOT of wrong information out there on REST.
That said, REST is not for everything. It's an architecture, so it's rather flexible how you can implement it. But if it doesn't make sense to access things primarily as resources, then REST may not fit, or it may only fit for parts of your application, which is fine.
