Definitions of local:

• noun:   public transport consisting of a bus or train that stops at all stations or stops

  Example: "The local seemed to take forever to get to New York"

• noun:   anesthetic that numbs a local area of the body
• adjective:   affecting only a restricted part or area of the body

  Example: "Local anesthesia"

• adjective:   of or belonging to or characteristic of a particular locality or neighborhood

  Example: "Local customs"

• adjective:   relating to or applicable to or concerned with the administration of a city or town or district rather than a larger area

  Example: "Local taxes"