I know iPhones (and iPads) run on ARM processors, which are little-endian by default (and iOS on itself is little-endian according to the Wikipedia page); however, ARM processors supposedly have the ability to switch between little-endian and big-endian. How possible is this and how does it work?
Endianness isn't something that end users have any real interaction with - but here is a 10,000 foot summary of what this means for users of Apple products.
In a nutshell - endianness for an internal processor is the same as the writing direction for a language. When you look at letters of an english text, we all agree to start on the top left and read first right then down. Other languages start on the right and read to the left and some even read down first before moving left or right.
It doesn't really matter to a user if the bits in an internal representation of an address or number gets stored little endian or big endian. In fact OS X on a Mac adheres to a big-endian representation and iOS adheres to little-endian ordering. This fact doesn't in any way mean that the two devices can't work together properly. This works because this representation only happens internally and doesn't get exposed to us as users.