Insofar as one could consider the kernel to be the core of an operating system, this (specifically, XNU on ARM) is the core of iOS. Having the Darwin userland atop that is simply icing on the proverbial cake.

What would you consider the core? Is it UIKit? Cocoa? libc? SpringBoard (the homescreen application)?

(Edited: s/Darwin/XNU/; thanks shibby!)