The Semantic Web is a collaborative movement led by the international standards body, the World Wide Web Consortium (W3C). The standard promotes common data formats on the World Wide Web. By encouraging the inclusion of semantic content in web pages, the Semantic Web aims at converting the current web dominated by unstructured and semi-structured documents into a “web of data”. The Semantic Web stack builds on the W3C‘s Resource Description Framework (RDF).

Also see linked data and knowledge graphs.

This Scientific American feature article from May 2001 sets out the vision (and yes, this is also a fun example of what a staid web page looked like in 2001):
The Semantic Web
A new form of Web content that is meaningful to computers will unleash a revolution of new possibilities
by Tim Berners-Lee, James Handler and Ora Lasilla

Also see:

Introduction to Semantic Technology

and for a slightly more skeptical point of view:

Web 2.0, 3.0 and so on

and this:

Why Adding Semantics to Web Data is Difficult