To localize is to focus on a small, specific area. The newspaper in your city might localize half of their news coverage, concentrating on just your state.
A doctor or dentist will localize pain treatment in certain cases, like when you get a novocaine shot in your gums before getting a cavity filled. Rather than a general painkiller affecting your whole body, this focuses only on the part of your mouth that's affected. You can also localize by adapting something to a specific location. A rural school might localize its schedule by opening later in the fall to allow students to help on family farms, for example.