The definition of "Web 2.0" is a disputed term which some people tout as a marketing term whilst others use it to refer to the transformation in web applications and services from the traditional means, some examples are the use of google adsense as opposed to the old style annoying pop ups and the huge flash ads down the side. Another example could be the change from internet explorer and netscape to browers like firefox and camino which include a wide range of new apps such as download managers, RSS etc. In terms of design, "Web 2.0" is usually referred to designs that are glossy and use a "roundy, thick" font and often have a reflective shadow. Some famous examples are the "Skype" logo and the web2go logo. So my understanding of the term Web 2.0 in a nutshell is really a synononym for "modern" and "innovative."
DISCLAIMER: I AM NOT AN EXPERT, SO SOME INFORMATION ABOVE MAY NOT BE TOTALLY ACCURATE.