In simple terms, what are the reasons for, and what are the differences between the GPL v2 and GPL v3 open source licenses? Explanations and references to legal terms and further descriptions would be appreciated.
The page linked to in another answer is a good source, but a lot to read. Here is a short list of some of the major differences:
internationalization: they used new terminology, rather than using language tied to US legal concepts
patents: they specifically address patents (including the Microsoft/Novell issue noted in another answer)
“Tivo-ization”: they address the restrictions (like Tivo’s) in consumer products that take away, through hardware, the ability to modify the software
DRM: they address digital rights management (which they call digital restrictions management)
compatibility: they address compatibility with some other open source licenses
termination: they address specifically what happens if the license is violated and the cure of violations
I agree with the comment about consulting a lawyer (one who knows about software license issues, though). In doing these things (and more), they more than doubled the length of the GPL. Although GPLv3 is a complex legal document, it was designed to be read and reasonably understood by software developers. There is also a guide to understanding it and an in depth discussion of the changes from v2 to v3 at http://copyleft.org/guide/.