First of all, marketing helps and when gadgets look cool, then people are drawn to them. Comparing the iPod to the generic USB-looking MP3 devices around at the time there was no comparison, the iPod won hands down.
Next is the interface, the early MP3 players either had an LCD screen, the later ones had a colour screen but really did not take full advantage of it. The iPod on the other hand displays song information and provides album covers and cover flow, which is a nice touch and ads to the user experience.
Next, user interaction - click buttons versus click wheel. This innovation made it easy for users to scroll through large songs lists and immediately raised the customer expectation. Once you've used it you'll never go back.
Finally, the complete end-to-end experience. For acquiring MP3 files, generic MP3 manufacturers leveraged off third party systems such as Windows Media Player. This proved to be problematic. Any problems users experienced due to software updates, upgrades, software errors, connection problems and so on were not considered to be the fault of the MP3 manufacturer, nor did Microsoft take any responsibility for the problems because it was associated with a third party device. No-one owned the user experience. Apple looked at the user experience from end-to-end and their response was to provide iTunes, an application which made it easy to acquire songs on iPods and other Apple devices.
Now the Apple iPod, iTouch and iPhone have become the defacto standard as mobile entertainment platforms and they have helped make Apple one of the most successful technology companies of the 21st century. Apple is definitely a good example of an outside-in company and this year, Apple was named 6th in the Millward Brown Optimor TOP 100 Most Valuable Global Brands 2009.