The semantic web refers to a set of work-in-progress technologies like RDF, OWL, and SPARQL that would allow for a greater semantic architecture throughout the Internet. Think of this as a more context-aware web, one where a machine can connect disparate systems without explicit programming.
In today's world, Google has perhaps the most robust semantic understanding of the Internet, but that understanding is based on amorphous blobs of text that Google must parse and analyze with sophisticated algorithms. In the semantic web, published content would provide its own context.
In a world of semantically connected content providers, a single software system could do all the disparate tasks a human can on the Internet, automatically, without programming or even human input.