Now that it's public knowledge that App Store submissions are being tested for use of private APIs, I need to ask the question... what exactly is a private API so that I may avoid them?
A private API is an API that is not documented in the SDK. For instance, a framework class might declare a method that is not intended to be used by outside developers. The behavior of a private API is not guaranteed. You can't even be sure that the method will be there in the future updates of the platform. Its declaration is probably not available in publicly distributed SDK header files. If you stick to things publicly defined in the SDK documentation, you'll be OK.