Humans can use the web to find specific information that they want because they understand what is written on each web page. Thus, whilst a search engine can find all the web pages with "matrix" written on them, only humans can easily distinguish those pages that are about the film "The Matrix" rather than about mathematics. The semantic web is a vision in which webpages are "understood" by computers, so that they can perform more of the tedious work involved in finding, sharing and combining information on the web.
Here is Tim Berners Lee (father of the World Wide Web) talking about the Semantic Web:
And here is another short introduction to the semantic web. All source material is on the Digital Bazaar wiki
More on the semantic web.