This rather unfortunate name conveys the sense of there being some new version of technology implementing the web.
That's not what it means though - it's usually used to describe particular kinds of web application, which use a collection of technologies and standards (which are not particularly new) to achieve their objectives.
Postmodern web would be a much better term to use.
It matters because language and terminology can shape the way we think about things. In the context of church websites, the postmodern web doesn't matter much, but the technologies associated with Web 2.0 most certainly do.
Martin Brasier, May 2009