The Semantic Web is a mesh of information linked up in such a way as to be easily processable by machines, on a global scale. You can think of it as being an efficient way of representing data on the World Wide Web, or as a globally linked database.
The Semantic Web was thought up by Tim Berners-Lee, inventor of the WWW, URIs, HTTP, and HTML. There is a dedicated team of people at the World Wide Web consortium (W3C) working to improve, extend and standardize the system, and many languages, publications, tools and so on have already been developed. However, Semantic Web technologies are still very much in their infancies, and although the future of the project in general appears to be bright, there seems to be little consensus about the likely direction and characteristics of the early Semantic Web.
What's the rationale for such a system? Data that is geneally hidden away in HTML files is often useful in some contexts, but not in others. The problem with the majority of data on the Web that is in this form at the moment is that it is difficult to use on a large scale, because there is no global system for publishing data in such a way as it can be easily processed by anyone. For example, just think of information about local sports events, weather information, plane times, Major League Baseball statistics, and television guides... all of this information is presented by numerous sites, but all in HTML. The problem with that is that, is some contexts, it is difficult to use this data in the ways that one might want to do so.