Why do fiber optic cables have the size they do? We all know that fiber optics are very small, but my question is, why are they small? Does it give them some advantage in transmission of data? If yes then how? What would happen if we make the fiber optics larger in size, or even smaller?
 A: If you're talking about a fiber optic as in fiber optic cables, consider this:They work on the principle of total  internal reflection to transmit electromagnetic  signals without losses. Now these have a certain critical angle(look it up),which is primarily a characteristic of the optic cable.However if you were to change the size, say diametrically, one would have to change the angle of incidence at which the light pulse would need to interact with the cable for long distances of transmission without loss. You might have noticed that such cables are really not so thick.
Hope this helps, pardon me if I went off track a bit.
A: A similar question has been asked here, but the answer isn't entirely complete. Yes total internal reflection describes larger diameter cables. But for some applications, a thin cable is better. For a thin cable, the diameter is near the wavelength of light. The wave properties of light become important. In this regime, people talk about the modes of a cable. 
One way to think of modes is that diffraction affects the shape of the beam as the beam progresses down the cable. The cable must be designed so that diffraction and the cable work together to keep the beam cross section constant. 
Another way of saying this is light is a propagating electromagnetic wave, and the fiber is the boundary condition of the wave. Modes are different solutions to the wave equation. They have different cross sections. 
A single mode is usually desirable because multiple modes propagate differently and get out of phase. Often the lowest mode with the smoothest cross section is the most desirable. 
For a more physics oriented description, here are some course notes on Optical Waveguides from the U of Rochester. If you aren't interested in details of solving Maxwell's equations, you still might find useful information about how waveguides are constructed. 
For a more commercial slant, you might try RP Photonics' Encyclopedia/Buyer's Guide. Here is an article on Modes, and here is one on Single-mode Fibers. 
