The adjective local describes something related a specific place. The potholes on a certain street in Pringle, Pennsylvania, might merit a story in the local newspaper.
Locate, location, locale — they all look and sound like local thanks to the Latin root locus, which means "place." Something that's local is limited to a specific place, like a particular neighborhood or city. Local also can describe places that aren't, well, places — they're more like areas. For example, a dentist might administer a local anesthetic to numb your mouth when filling a cavity. That means the anesthetic acts only on a specific area of the body.