Microfiber is Polyester
Microfiber is polyester. It's synthetic (it's made from chemicals). The only difference between microfiber and the polyester suits from the 70's is that microfibers are extremely small. This makes them great for absorbing water as cleaning cloths, but it also makes them very soft to the touch and durable.
Because microfiber is synthetic, it has to be cleaned differently. Solvents that will hurt cotton will do nothing to microfiber. However, things that do nothing to regular cloth will damage microfiber. Also, certain chemicals will literally dissolve the chemicals that make up microfiber, so don't just put anything on your furniture!