Webster's dictionary defines "paradigm" thus:
However, we commonly refer to a paradigm as a set of deeply related ideas. A paradigm isn't an example, but a projection of thought. When you work in paradigm as opposed to another, you think differently than as if you were in the other.
In programming, two distinct paradigms would be object-oriented programming and logic programming. Smalltalk vs. Prolog.
So, a ParadigmShift is when you move between two paradigms.
Typically, a ParadigmShift is lauded when it completely changes the world as we know it (or promises to). Usually they are liberating because they allow one to solve an entirely new class of problems that previously were either impossible or extremely difficult to solve. I suspect paradigm shifts only occur when the old paradigm produces a critical mass of hard problems that forces a whole new technique to be created.
If you consider the whole set of ideas to be an evolutionary system, ideas would then be subject to PunctuatedEquilibrium?. It would seem this is the case, and the punctuations are marked by ParadigmShifts.
Note, when you make a shift, you are only trading one set of ideas for another. The two may intersect in any way (including being a subset or a superset of the other, or being mutually exclusive). However, over time, certain points in the ideaspace become extinct. In other words, we forget things, like how we built the pyramids of Egypt, for example.
Since people like to hang on to their world views because without them there is no structure to their existence, they do not appreciate someone supplanting their paradigm with another. Consequently, when they are violently forced to switch paradigms, they tend to explode... an event that ScottAdams? calls (in the DilbertCartoon?), "a paradigm shifting without a clutch." ;)
[This has been lifted wholly from Wiki:ParadigmShift]