I noticed that there is software (such as iExplorer) that allows you to access files on an iPhone-device from your Mac.
Now my question is: How can I access
Unfortunately, there's no easy or legal way to access files on your iPhone, especially through Objective-C.
The applications installed on iOS are sandboxed, which means they can only access files in their own directory tree; they have no access/knowledge of other files.
Like you said, you can access files using software like iExplorer, but not programmatically from the iPhone itself.