The Semantic Web is an extension of the Web where data is given explicit meaning. This allows the data to be integrated, processed, shared, and filtered with much greater ease than before. The idea was popularized by Tim Berners-Lee, who was pursuing this goal since the very first draft of the World Wide Web itself.
The technical foundation of the Semantic Web is given by the standards RDF - Resource Description Framework (for data description), OWL - Web Ontology Language (for giving the RDF terms a formal meaning), and SPARQL - Protocol and RDF Query Language (as a query language and protocol).
A not too simplified view of the Semantic Web is to think of the Semantic Web to traditional databases like the Web was to hypertext systems.