It's an extension of, not a replacement for, the World Wide Web.
Anakin Skywalker is Luke Skywalker's father.
It's easy for you to figure out what this sentence means -- Anakin and Luke Skywalker are both people, and there is a relationship between them. You know that a father is a type of parent, and that the sentence also means that Luke is Anakin's son. But a computer can't figure any of that out without help. To allow a computer to understand what this sentence means, you'd need to add machine-readable information that describes who Anakin and Luke are and what their relationship is. This starts with two tools -- eXtensible Markup Language (XML) and Resource Description framework (RDF).
That probably sounds a little abstract, and it is. While some sites are already using Semantic Web concepts, a lot of the necessary tools are still in development.