Otherwise known as a burr mill, a burr grinder utilizes two burrs (rough edges) to grind coffee between a moving wheel and a surface. More expensive than a blade grinder, they result in high-quality coffee grounds. You can either have manual or electric grinders, and the difference is largely self-explanatory. Electric burr grinders are more efficient, while you can control your grind size with a manual grinder.
To clean your grinder, unplug your coffee machine, remove the grinding chamber, and remove the burrs. You can do so by twisting them out of place. You can leave the inner burr inside the machine and clean it with a cloth. Use your finger or something with bristles, like a toothbrush, to remove coffee particles from the machine and burrs. Be careful around the sharper edges of the burrs. There are also burr grinder cleaning pellets that you can use.