A small addition to Rob’s definition, it helps to think of Web 1.0 as an extension of the traditional publishing model of things like newspapers, books, radio and television… they are one-way forms of communication. The author creates the content then publishes/broadcasts it while the audience can only receive. Or put more simply, I talk, you listen.
Web 2.0 gives the audience the ability to not only participate in TWO-WAY communication (responding or replying to the content, often in real time) but often also to CHANGE or MODIFY the content itself. Wikipedia is the obvious example. A content creator publishes content, the public can interact with, change, or discuss the content on the fly. Very Cool.