iPhone Explorer is an attempt at giving users a traditional file manager for iOS. With iTunes and this installed, simply plug in your iPhone or iPod and browse your files.
The theory is great - iOS is a very closed system compared to a traditional operating system - and many users would love to have more control. When your device is plugged in, a traditional file tree will appear on the left panel of iPhone Explorer. You can then browse content at your leisure.
iPhone Explorer also allows you to create folders on your iPhone, and drag files in and out of them as if it was a normal storage space. That is the theory, though, unfortunately, iPhone Explorer is riddled with problems.
Browsing your iPhone's file tree is really awkward, as files are named in odd ways. Your music library, for example will be unrecognizable. Photos too are hidden in such a way that you can't use iPhone Explorer to access them. The application is also unstable, and has a tendency to crash if you attempt to move files. Lastly, of course, changing the file tree could damage the functionality of you device.
If you want to use your iOS device as storage, something like USB Disk is perfectly functional, and much more stable. iPhone Explorer is a good example of a nice idea that doesn't work well in practice.