2001 was a banner year for Apple products. Perhaps the most important of these was unveiled on October 23, 2001. The iPod was Apple's answer to the portable music player also known as an MP3 player, a reference to the popular music format used to transfer and share music at the time.
Apple was looking for products to help drive sales of Macintoshes. At the time, iMacs were popular computers in college dorms, and Mac users were trading MP3 music left and right. Apple wanted to add a music player that would be a reason to continue to buy iMacs, at least for the college and younger crowd.
Apple started by looking at existing music players, possibly with the goal of acquiring the company that made them, and rebranding the players as its own. But Steve Jobs and company couldn't find any existing product that wasn't too big and clunky, too small, or didn't have a user interface that was “unbelievably awful” (a comment possibly made by Steve Jobs at the introduction of the iPod).
So Steve said go forth and build me a portable music player. And they did. And the rest is history.
Oh, the iPod name? Rumor has it the name came from a copywriter who was reminded of the pods in the movie '2001: A Space Odyssey' when he saw one of the prototypes.