What's with the "i" on Apple's product names?

After reading soooo many news about the latest craze to hit US- Apple's iPhone... i'm curious now as to why Jobs and his company named their latest products and services with the "i" in the beggining... iMac, iPhoto, iLife, iPod, iTunes, iPen, iPhone and iHavenoideawhatelsethereis... I can understand the "e"+something like e-commerce, e-living, e-banking - it simply means electronic... but what's with the "i"? hmmm... eniweys if you're not familiar what the iPhone is watch this funny video review by Pogue of New York Times.