The click wheel UI of the iPod made its large storage actually useful rather than just being a bullet point on a box. If you had a thousand songs loaded on your iPod it was pretty easy to navigate to any album, artist, or playlist.
Most other PMPs (even after the iPod) had UIs that were basically lifted from the Walkman. Navigating HDD players was a pain in the ass.
Besides the click wheel UX the iPod had iTunes doing the heavy lifting of library management. It made editing and adding metadata to songs, which helped organize your library, very easy. That same organization completely carried over to the iPod. iTunes also supported automatically syncing an attached iPod so if you ripped a CD it appeared on your iPod after plugging it in.
Most of the competing HDD based PMPs were obsessed with just acting as mass storage devices when attached to a computer. So they had painful on-device UIs dealing with the multitude of differing naming conventions and poorly tagged files.
So while HDD players weren't invented by Apple they:
1. Made an HDD player small enough to fit in a pocket competing in dimensions with Flash based players.
2. Made a UI that allowed easy navigation of a large library.
3. Used a high speed connection that made it trivial to fill the large storage. This same connection also charged the device.
4. Had a very responsive UI not limited to the seek speed of the internal HDD. The iPod let iTunes do the hard work of creating the on device database. The iPod OS didn't need to go read metadata from every file to populate menus or display song information. It did the hard work once (in iTunes) and just used the database for everything but audio data from then on.
Upgraded to a Zune after the battery on my Zen died. The screen and UI were great imo, sad it didn't stick around.