I agree with the fact that RDF is mired in confusion. Thus, let’s try to bring clarity to this important matter via this discussion thread, or at least make a contribution to said endeavor :)
RDF is an Abstract Language. As a Language, it uses a combination of signs, syntax, and semantics to encode and decode information (data in some context). In a nutshell, it is simply an open standard for creating digital sentences using a variety (rather than single) notation.
In regards to the notion of a Semantic Web, you simply construct RDF sentences/statements where hyperlinks (HTTP URIs) are used to identify the subject, predicate, and object (optionally) of a sentence i.e., using Linked Data principles (which is simply about naming things using hyperlinks and describing things using subject->predicate->object or entity->attribute->value sentences).
Unbeknownst to many, the Web has been a Semantic Web since inception. By that I mean: HTML enabled every publisher to unambiguously identify a document using a hyperlink and at the very least indicate it was related to some other page (also unambiguously identified by a hyperlink).
Here an example of what’s stated above via a collection of RDF sentences (using RDF-Turtle notation):
<#thisPage> a schema:WebPage .
<#thisPage> xhv:related <#someOtherPage> .
Using a Semantic Web browser extension, here is a visualization of the sentences above.
Note, if you install the extension, the exploring the full power of RDF and the notion of a Semantic Web will be reduced to a single click :)
The problem for RDF is basically not having tools built for in on the client side due to the initial complexity of writing portable browser extensions.