The police is a minor group of the World Government. They consist of normal officers and the Special Forces, who are very skilled battlers and are connected to the Top Brass somehow.
While the Marines maintain a high order of policing in the world, worldwide police officers are employed by the World Government to supervise local areas and arrest unlawful citizens.
Unlike the Marines that sails on seas, the policemen can't sail so they must stay on dry ground.
The duty of a police officer is to maintain law and order, however they only deal with local interests unlike the Marines who maintain a global presence across the world. They leave the task of capturing tough criminals to the Marines, but aid them where needed. So far they have only deployed in small numbers which sharply contrasts the scale of deployment of the Marines.
The police forces across the world seem to be independent of any ranks, mostly due to the fact Oda has yet to release any ranking system for them. However high ranking officers seem to wear a long coat, much like the HQ rank and above Marines.