Microfiber can be composed of many parts, most commonly in the detailing / car care industry we use a combination of polyesters and polyamides. These
microscopic laboratory born fibers are around 1/100th the diameter of a human
hair, this ultra fine thread is what gives microfiber its delicate touch and
super soft feel. To put that size into perspective, if you were to think of a
regulation basketball as the equivalent of the diameter of a human hair, an
individual strand of microfiber would be smaller than an M&M chocolate
Why is this important? While you might see a fluffy towel with your naked eye on a microscopic level there is a very tiny, but very uniform and durable strand there. Almost all microfiber will share an identical fiber structure, regardless of weave or pattern. How the fibers are laid out will impart different characteristics to the material (plush for delicate surfaces, waffle weave for drying, flat for glass, suede for coatings, etc)
Each individual strand has a star-like structure and all strands are virtually identical across the entire surface of a towel. If you could pull a fiber from one towel, and another from a different towel of similar quality and cross section them you'd likely not be able to tell them apart. This leads to a uniformly soft towel that performs the same regardless of fold or what portion is in contact with the surface. This is in stark contrast to the wild inconsistency of cotton fibers which can vary in shape and size from one strand to the next.
The star shaped structure on each strand allow microfiber to trap small particles, dirt, moisture and debris making them very effective for cleaning. Compared to the inconsistent, tube-like, shape of cotton which is absorbent, but not ideal for cleaning microfiber has a clear advantage.