It started with iMac, which was named for it's easy access to the Internet at a time when other computers required rather elaborate set ups. Apple discovered that there was an element of "coolness" in the name & used it for other products & software (iTunes, or iPhoto,the photo program bundled with Mac software, for instance.)
According to Wired, a guy who helps companies name products "said the name is a stroke of genius: It is simple, memorable and, crucially, it doesn't describe the device, so it can still be used as the technology evolves, even if the device's function changes. He noted the 'i' prefix has a double meaning: It can mean 'internet,' as in 'iMac,"' or it can denote the first person: 'I,' as in me."
According to the same article, Vinnie Chieco, the guy who came up with the name iPod" kept thinking about Steve Jobs strategy that "The Mac is a hub, or central connection point, for a host of gadgets." So
This prompted Chieco to start thinking about hubs: objects that other things connect to.
The ultimate hub, Chieco figured, would be a spaceship. You could leave the spaceship in a smaller vessel, a pod, but you'd have to return to the mother ship to refuel and get food. Then Chieco was shown a prototype iPod, with its stark white plastic front.
"As soon as I saw the white iPod, I thought 2001," said Chieco. "Open the pod bay door, Hal!"
Then it was just a matter of adding the "i" prefix, as in "iMac."...A source at Apple confirmed Chieco's story.