Fiber optic has been in the news recently where the NSA has been picking up the calls and email messages of people. However this is not simple to do.
Fiber optic is a type of cable to connect computers (and phones) together. Instead of using copper that was normally used, it uses strands of hollow glass. The glass strand within it is really thin which is then wrapped in plastic and sometimes in Kevlar which makes it stronger and less likely to break. Fiber optic cable and equipment is more expensive and harder to set up than copper cable and its equipment.
The information is sent across the fiber optic by light signals. This makes it much faster than metal media such as copper but it is not as flexible to use as copper. You are seeing more fiber optic run down the streets these days (usually it is spools of orange cable you see being buried recently). It is sometimes put on poles but usually in the ground. In some places they run fiber optic cable to the house. Fiber optic cable has been used for years to connect the large distribution points on the Internet and connect country to country.
With copper it is easy to eavesdrop as you just need to put equipment near the wire and you can pick up the signals in the air. With fiber optic you must break the line and insert a piece of equipment and not break extra glass and then put it back together and in the meantime the sending and receiving ends know the signal was interrupted.
Normally what is done when eavesdropping on fiber optic cable is you have gotten access to the equipment at one end or the other end of the line and listened in through there. Fiber optic cable is much more secure than copper and much faster. Usually when someone has gotten signals from fiber optic cable either the providers at either end allowed them to listen or they illegal accessed those companies equipment.