A small note, these slides are the ones as delivered at PyOhio (which was also recorded), which are slightly updated from the ChiPy talk.
It always amazed me how a python implementation in python can be so much faster then the original python implementation in C. I didn't take a deep look at pypy, it's sounds like magic :P
It's hard to describe exactly what PyPy does, but it's more of a JIT / interpreter generator.
You write a language using RPython (which is more static than regular python), and PyPy makes a VM for it, or can turn it into C, or CIL, or...
Python on PyPy is the same way.
It makes experimenting with new ideas and languages very easy, and (IMO) that is the primary reason for PyPy's existence; faster Python execution is a side benefit.
They use a subset of python called RPython for implementing pypy.
pypy and pypi, it took me the longest time to remember which is which