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.
So it seems that you're looking for an API which makes it possible to access the filesystem of the iPhone from a computer. Well, this API exists, and it's called the MobileDevice framework.
Here is an old project to browse the iphone. You may be able to get some pointers from it on building an application to do the same with the latest info.
http://code.google.com/p/iphonelist/
Couple that with carbonic acid's post about the Mobile Device Framework and you should be able to do some good stuff.
if I find more unique info ill post it here.