The Arduino module is a simplified microcontroller board. Although there are an increasing number of alternate form factors, the original design includes all the electronic parts necessary to power and communicate with the microcontroller: regulator, clock crystal, USB-to-serial interface, and SPI programming interface for replacing the bootloader. Alternate design should include these elements as well, or show how to add them easily.
Arduino is more than a piece of hardware. It's also the software that lets you program and communicate with it, the documentation and tutorials that explain how to use it, and the community that can help you when you have trouble. It's the fact that all of these work together that, more than any individual piece, makes the project useful.