Light is sent into a thin fiber. When light strikes a surface two things can happen, it can exit the first material or reflect back. If the light is in a material with a higher index of refraction, think of glass as higher than air, then the light that exits bents closer to the surface. If the light is initially traveling at an angle close to parallel to the surface, there is no way to have the light bend enough, so a full reflection occurs. So, light in a thin fiber reflects back into the fiber, since the light strikes the walls of the fiber at small angles.
In communication the frequency of a laser is used to determine which conversation is which. The lasers change frequency rapidly in response to voltage changes, and hence can carry many signals at once. The signals are chopped into pulses, or digitalized, so one fiber can carry thousands of signals with pulses of different frequencies following each other. The original wave an be reconstructed from these pulses.
In decorations the signal does not need to carry communications, so there is no need for a laser. An LED will do just fine. The light travels through the fiber even if it is bent. The reflections still direct the light along the fiber through the bends. Actually, this also happens in communication fiber optics.
Unlike communication fibers, air is fine to replace the second layer of glass, called cladding. The cladding protects the fiber from loss due to things like drops forming on the glass, but in decorations a little light escaping is no big concern.
Also unlike communication fibers, the fibers used as decorations work with all colors. Color is determined by the frequency of the light. Communication fibers do not use two bands of frequencies because the light is absorbed for them. But, since decoration fibers are short enough all frequencies of light get through. The absorption is caused because glass making uses water, and the water cannot be totally removed from the fiber. Some of the water breaks down, and the hydroxyl is what does the absorbing.
Fiber optic decorations also do not suffer from scattering, it actually is what makes the fiber visible. In communication, the loss due to scattering is a problem. So, special glass is not needed for decorations.
So, fiber optic decorations can be made cheaper than fiber optic communication cables with less attention to detail. Actually, it is better to have scattered light in decorating.