How do people hack iPhone games so easily?
iOS applications store their data in files that are available from a computer in two easily-accessible ways:


Inside an iTunes backup
Via a MobileDevice-framework-based tool such as iExplorer


In my experience, game save data is stored in a fairly ordinary property list file that is manipulable via the plutil tool.  The data can be restored and replaced without any code knowledge.  From there it's a simple matter of how much the app trusts its save data.

For an example of how this can be used not just for high scores, but to cheat at a game, see the Nimble Quest iOS Trainer, which is itself MobileDevice-framework-based.

(The MobileDevice framework is an Apple private framework created for iOS device access, which has been reverse-engineered to enable the creation of iOS device tools not available from Apple.)