Microfiber used for cleaning products is a very thin synthetic filament (a fiber about the size of a human hair) that has been extruded with two synthetic polymers — polyester and polyamide (nylon). These fibers are bundled into strands barely visible to the human eye and then spun into yarn, or thread, which is then woven or knitted into cloth fabric of tiny "hooks & loops" by machines. During the manufacturing process, those bundles are split into even finer single fibers (estimated to be at least 1/100 the size of a human hair) using a specific combination of chemicals, heat and agitation. When examined under a microscope the bundled strand appears star-shaped with wedge-shaped polyester filaments surrounding a nylon core.
These split fibers are the source of microfiber's magical cleaning ability, and the number of splits determines the quality of the microfiber cloth - the more splits, the more surface area with lots of nooks and crannies and the more absorbent, effective at scrubbing, and amount of dirt it can trap and hold.
Traditional cleaning textiles like cotton or wool work by either absorbing soil which has been dissolved and emulsified by cleaning chemicals and water or pushing it into the air. Dirt which is not emulsified is not easily picked up.