At first, it wasn't dominant. But it was a little better in a lot of ways - better integration, smaller size, better aesthetics, better interface.
Based off of those (admittedly not overwhelming) advantages, the ipod got relatively popular. And then it became a pop icon.
That's really the story here. It's better than anything else out there, but it's not THAT much better. Come on; I have 2 ipods (shuffle and mini) and am as much of an apple fan as anyone, but there are other good players out there. Maybe not quite as good, but good enough that if the market was divided simply by quality, apple would have a good share, but not market domination.
But it's part of pop culture now; it's cool. At a certain point these things take on a life of their own.
When ipods
first came out I was blown away, and wanted one (and eventually got a 1st gen 5 gig

). But a lot of other people, including people who now have ipods, just laughed at me, "taken with yet another apple product." They knew what it did, but it wasn't until it became a part of the culture that they actually wanted one.