To put it very briefly, the material we know as “carbon fiber” is actually a mixture of long, woven threads of crystallized carbon atoms (graphite) impregnated with a plastic resin. It is sort of like dipping a piece of canvas into a bucket of glue and letting it dry. The carbon threads are only a tiny fraction of the width of a human hair, which means their are MILLIONS of them packed into very dense spaces.
Depending on the weave of the sheets, carbon composites can have varying levels of tensile (stretch) strength, and modulus (stiffness). The reason that carbon fiber has become so popular in the sports and transportation industry is because of its excellent strength-to-weight ratio (higher than nearly all metal alloys) and its fabled rigidity.
The sheets are layered in different directions (like plywood) to form tubes and other rigid shapes. This is called the “layup”. Because they are stronger along the long axis of the graphite threads, the carbon sheets are usually added in at least eight layers, each one rotated in a different linear direction depending on the application of the tubing.
Once the sheets or tubes of carbon fiber are layed-up and molded into their intended shape, they are heat-treated at temperatures well over 1,500 degrees, which increases their strength considerably. Currently, the majority of all carbon fiber in the world is manufactured by only five major companies.