One of the really great things about the Arduino design is that it is open - all the circuits and board designs are available for anyone to use. One key upshot of this is that once you have done some experiments with something like an Arduino Uno or Mega, and decided on how you want your circuit idea to work, you can easily re-create just the bits you need, in whatever shape suits your project. There are lots of people who have built their own "Arduino" on hand-soldered stripboard or even on a solderless breadboard. Adding extra components and your own wiring is just as easy, and there are plenty of tools to help you design printed circuit boards too.
In short, Ardiuno is not only a fun platform for learning about electronics and programming, but also scales smoothly into real products, if your idea is good enough!
Great question, and I can honestly say its one of the most useful tools for REAL projects. The AVR is very powerful and the Arduino simply gives you an approachable handle into its world. Sure, its also a great learning tool, but it's so elemental in so many real world projects. Happy to share personal examples if youd like...
If I were working on a microcontroller based product, one with a target volume in the thousands, I'd prototype it using an Arduino, but production builds would only use the AVR microcontroller, and the specific parts my product uses. The Arduino is more than just a raw microcontroller. Some of the parts that make it great for learning and prototyping are not needed in general, and add costs to any high volume product.