optical fibers simply guide pulses of light, whereas electrical systems use wires to guide electrical signals. the light signals are then interpreted. its just another way of transferring data.
as far as easy projects go, I really have no idea. optical stuff is generally harder to work with and more expensive, as its an emerging technology. I mean, i guess you could get an optical fiber and put one end near an LED and one end near a photoresistor and transfer some data that way, but its not really the same thing...