What does the "i" in Apple product names mean?
When Steve Jobs first introduced the iMac in 1998, he proclaimed that the i stood for Internet. Jobs went on to say, "i also means some other things to us" and displayed a presentation slide with the keywords:


  internet
  individual
  instruct
  inform
  inspire


You can even view video of this event.

The "i" was first used on the iBook and iMac. These were produced as Steve Jobs wanted a pro and consumer model of a desktop and portable computer. This later rolled out with more products, iSight, iPod, iPhone, iPad.

Yes the products are trademarked, but using an "i" itself before a product is not trademarked and it cannot be. Here is Apple's trademark list