The article doesn't provide a provide a definition of Science 2.0, but roughly the suggestion is that scientists will begin to do their work with open data, lab notes, results, etc. in ways that allows for this work to be viewed and commented on by others.
The most discussed example is MIT's OpenWetWare, which is a wiki designed for biologists to open their laboratories to others and share information.
There are a lot of issues to work through, but this quote sums up my feelings about this effort:
"the real significance of Web technologies is their potential to move researchers away from an obsessive focus on priority and publication, toward the kind of openness and community that were supposed to be the hallmark of science in the first place."