Microfibers are able to attach themselves to even the smallest, most microscopic dirt particles, however normal cotton cloth fibers crudely brush past.
Below are the reasons why the performance of microfibers better:
1. Material: The cloth are made of tiny wedge shaped fibers, up to 100 times finer than a human hair. The tiny fibers grab and hold dirt.
2. If forces were visible, you'd be able to see that there are adhesive forces between microfibers and dirt. Although there is only a microscopic amount of van der Waals force between one microfiber and any given dirt particle, remember that there are millions of microfibers in a cloth, so the overall sticking effect is magnified dramatically. That's why dirt, dust, and other stuff can be "hoovered up" by microfiber cleaning cloths.