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 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 addressed compatibility with some other open source licenses
termination: they addressed 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. GPL 3 is many things, and one of them is that it is a very complex, technical legal document.