Basically, your data, voice and video is digitalized and modulated to travel over laser light using one of the multiplexing techniques: Time division, frequency division or Wavelength division multiplexing. Then its all upto the fiber to carry it across to the other end. Total internal reflection ensures that it always stays inside the cable, even through bends.
The optical fibers can carry signal upto 50kms without need of any special equipment. Beyond that it needs to be amplified and reconstructed to reduce errors, such thing is done by devices called repeaters.
Checkout an easy explanation of how Optical Fiber Cables work, (its easier than the text above):
The video explains how Total internal reflection is the property of every liquid and solid when light travels through it. The explanation goes onto how fiber carries the light signal, how it encodes and decode PCM signal and so on.
More Technical explanation taking physics concepts into consideration: