How does css3pie work?
What is happening behind the scenes with css3pie that makes it so IE can use css3 features?
The CSS3Pie website has a lot of detail, but I'll try to explain a bit.
In the case of CSS3Pie, it implements several features which are missing in IE. These are border radius, box shadow and linear gradient.
At the end of the day, it is a hack. It doesn't actually add new features to IE; it merely makes some existing IE features work in a slightly more standard way.
If you want to dig deeper, CSS3Pie is open source so you can study it. It is quite complex code, though, so you may find it easier to look at some of the other (simpler) HTC files that are also available.
Before CSS3Pie, there was already one available from HTMlRemix.com which offered rounded corners and worked in a very similar way to CSS3Pie. CSS3Pie is a better piece of software, but you may find the HTMLRemix code easier to understand.
There are also a few others you may want to look into:
Whatever:Hover fixes IE6 so that the CSS :hover feature works with all HTML elements rather than just <a> tags.
IE PNG Fix makes older versions of IE work better with PNG graphics with transparency.
Hope that answers you question.