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.
Semantic Web Applications
Unfortunately, the Semantic Web is dissimilar in many ways from the World Wide Web, including that you can't just point people to a Web site for them to realise how it's working, and what it is. However, there have been a number of small scale Semantic Web applications written up. One of the best ones is Dan Connolly's Arcs and Nodes diagrams experiment:-
One of the objectives of the advanced development component of the Semantic Web activity is to demonstrate how RDF and Semantic Web technologies can be applied to the W3C Process to increase efficiency, reliability, etc. In the early stages of developing an RDF model of the W3C process, the tools I was using to visualize the model while working on it started working well enough that I started applying them to all sorts of stuff.