A majority of carbon fiber is made from Polyacrylonitrile (C3H3N) also known as PAN. First it goes through a process called spinning, where the PAN is extruded into small fibers. During this process it is run through a bath to solidify the fibers then stretched and washed. After this the fibers are put through a process called stabilizing also known as oxygenation. It is stretched over hot rollers till the desired levels of oxygenation are reached. The fibers are ran through an over at over 1000 degrees Celsius in an environment that is low in Oxygen in a process called carbonization. This allows the fibers to release the Hydrogen and Nitrogen atoms without burning the fiber. Once the desired outcome is reached in the carbonizing process the fibers go through a surfacing process. After carbonization the fibers do not bond well with epoxies. Because of this the surfacing process scuffs the fibers and oxidizes to allow for a better bond. The last process before packaging is known as sizing where the fiber is then coated to protect them from further processing. 
After the carbon fiber has been created it is typically rolled onto cylinders called bobbins. Thread counts, also known as K counts, are the number of fibers in a single strand of carbon fiber tow. Typically, this is between three to twenty-four thousand fibers per stand. For instance, if you had 3k carbon fiber tow it would have 3,000 fibers wrapped together, if you have 6K carbon fiber tow it would have 6,000 fibers wrapped together and so on. 
Once we have the carbon fiber tow we can do a few things with it. First it can be wound. In this process you would take your continuous carbon fiber tow, draw the tow through a resin bath then wrap tow around a spool to the desired thickness and length. This can be used to make carbon fiber tubes or even tanks. You can also chop the fiber into little pieces. You would then scatter your chopped carbon fiber in a mold and add resin close the mold and depending on the resin used you could heat or simply just wait till the part is cured. 
Lastly there is carbon fiber weave, also known as carbon fiber mesh. In this process you could take the carbon fiber tow and introduce it to a loom. The fibers would be woven together like a blanket. There are several ways to do this depending on the application you are seeking. There is plain weave where one tow is woven over one tow then under the next in both directions. Similarly there is a twill pattern where, like the plain weave the individual tow is woven over and under a tow in the opposite direction. However, with twill we can request a change in pattern. A 2x2 twill for instance will weave the tow under two tow in the opposite direction then over the next two and repeat in both directions. There is a 4x4 twill that would have the tow weave over four tow then over the next four in both directions, and so on. This allows for the cloth to be more formable but has a tendency to fray and fall apart. There is also harness weave which would give you an imbalance on your weave. In the case of “5 harness satin” the tow would be woven over five tow in the opposite direction then under just one. This would be repeated in both directions. This allows for more stiffness in one direction than the other.
There are also unidirectional mats as well. In this case the fibers all run in the same direction. However, because of this there needs to be some type for stitching or a small amount of resin infused as there is no weave pattern to hold the sheet together. Similarly, there are multiaxial where you have multiple layers of unidirectional that do not necessarily go in the same direction. In the case of plus or minus 45 degrees you could have two layers of unidirectional 90 degrees from each other one at positive 45 degrees the other at negative 45 degrees.