A warrant for arrest is a legal document instructing law enforcement to take you into custody.  It is issued by a judicial official, usually a magistrate, when he determines that there is probable cause to believe that you committed a crime.  An officer can arrest you if he has a warrant for your arrest or if he knows a warrant has been issued, informs you of it and serves it on you as soon as possible.

For example, a person who claims you have assaulted him or her may go to the magistrate, make a statement under oath, and have a warrant issued for your arrest.

City police may arrest you in their jurisdiction in the city or anywhere within a mile of the city boundary.  Sheriff’s Deputies or County Police may arrest anywhere in the State for a felony committed in their county.