The Semantic Web is just that - a Semantic (meaningful) layer on top of the WWW. It is semi structured (RDF), it is self-describing (ontologies using OWL), and allows resource discovery (SPARQL).
The Semantic Web works on the premise of the "Open World" assumption; just because something is not stated doesn't mean it doesn't exist, it is simply "unknown". This is a fundamentally different logic to that used in an RDBMS like MySQL et al. - if something is missing it doesn't exist - "Closed World" assumption. Prolog and DATALOG are good examples of Close World logics.
If you want to really learn what is happening underneath, you'll need to look at its foundations, which lie in Description Logic. A good overview of the Description Logic can be found here: http://www.inf.unibz.it/~franconi/dl/course/
If you want to learn more about RDF, read the RDF Primer. RDF Semantics is another rip-roaring read.
Researchers have basically given up on the "Semantic" part of the Semantic Web and decided to focus on Linked Data - how RDF triples can be navigated so that we can waste more Internet bandwidth ;-)