You're struggling because there are two relatively different understandings of the term "REST". I've attempted to answer this earlier, but suffice to say: Twitter's API isn't RESTful in the strict sense, and neither is Facebook's.
sTodorov's answer shows the common misunderstanding that it's about using all four HTTP verbs, and assigning different URIs to resources (usually with documentation of what all the URIs are). So when Twitter is invoking REST they're merely doing just this, along with most other RESTful APIs.
But this so-called REST is no different than RPC, except that RPC (with IDLs or WSDLs) might introduce code generation facilities, at the cost of higher coupling.
REST is actually not RPC. It's an architecture for hypermedia based distributed systems, which might not fit the bill for everyone making an API. In the linked MSDN article, the hypermedia kicks in when they talk about <Bookmarks>http://contoso.com/bookmarkservice/skonnard</Bookmarks>
, the section ends with this sentence:
These representations make is possible to navigate between different types of resources
which is the core principle that most RESTful APIs violate. The article doesn't state how to document a RESTful API and if it did so, it would be a lot clearer that clients would have to navigate links in order to do things (RESTful), and not be provided with a lot of URI templates (RPCish).