(Latin: political or geographical division)

1. An area of a town or country, especially one with a distinguishing feature or one that is an administrative division.
2. A portion of territory specially set off or defined; such as, for judicial, political, educational, or other purposes.
3. One of the territorial areas into which an entire state or country, county, municipality, or other political subdivision is divided; for judicial, political, electoral, or administrative purposes.

Properly, a limited extent of a country; a circuit within which power, right, or authority may be exercised, and to which it is restrained.

A word applicable to any portion of land or country, or to any part of a city or town, which is defined by law or agreement. A governor, a prefect, or a judge may have his district.

Some of the states are divided into districts for the choice of senators, representatives, or electors. Cities and towns are divided into districts for various purposes; such as, for schools, revenue collections, etc.

district attorney
The prosecuting officer of a Federal or State judicial district in the U.S.
district energy, district heating, district cooling
A term for energy; such as, steam, hot water, or chilled water; which is produced at a central location and then transmitted to various specific sites in a given area (district) for uses; such as, space heating and cooling, or domestic hot water heating.

Such a system can substitute for furnaces, air conditioners, etc. within the district's individual buildings.

district judge (s) (noun), district judges (pl)
A high-ranking court officer, or a public official, who presides over a U.S. Federal or State court.
District of Columbia (D.C. or DC)
A Federal district, the capital of the United States; coextensive with the city of Washington on the Potomac River.
To divide into new districts, especially to give new boundaries to administrative or election districts.
The redrawing of the boundaries of legislative districts for electoral purposes.
Red-Light District
1. Relating to the part of a town or city where brothels and other commercial sex-based activities are concentrated.

From the red lights traditionally displayed in the doors and windows of brothels. Note: there is no explanation in the dictionary as to why they "displayed" the "red lights".

Encarta World English Dictionary.

2. An area or district in a city in which many houses of prostitution are located [1890-95; allegedly so called because brothels displayed red lights].

At least in the U.S., some say the origin of the red light comes from the red lanterns carried by railway workers, which were left outside brothels when the workers entered, so that they could be quickly located when the trains were ready to leave.