The reason that the letter i was originally used, back in the 90s, was that the internet was new, and people wanted a simple computer that they could mostly use to hook up to the internet. Hence, the iMac (the internet Mac) was introduced.
That was a long time ago, and it turned out that people liked the iMac, which of course connected to the internet the same way that all other personal computers did. But the i was kind'a catchy, so it was used as part of the name of a little music device that wasn't even connected to the internet, the iPod. And so it went.
My opinion about this is that since the internet was so cool and exciting, that just using the i was going to be catchy, even if it really didn't have anything to do with the internet. When radio was all the rage, a little red wagon was named a *radio flyer*. Really, go Google it, I'm not kidding. Nothing to do with radios, it was just picking up on the glamour of that new technology.
So there you go. I noticed that Apple TV doesn't have an i in the name, which shows that Apple is making an attempt to break away. Getting the i out of the iPhone, and maybe naming it an ApplePhone, or a MacPhone, would make more sense, so at some point that should happen, too.
Then all of this will be old history trivia, which it kind'a is already.