Downtown is a term primarily used in North America to refer to a city's core, usually in a geographical, commercial, and community sense.
The term is thought to have been coined in New York City, where it was in use by the 1830s to refer to the original town at the southern tip of the island of Manhattan. As the town of New York grew into a city, the only direction it could grow on the island was toward the north, proceeding upriver from the original settlement (the "up" and "down" terminology in turn came from the customary map design in which up was north and down was south). Thus, anything north of the original town became known as "uptown", while the original town (which was also New York's only major center of business at the time) became known as "downtown" or "Lower Manhattan". During the late 19th century, the term was gradually adopted by cities across the United States and Canada to refer to the historical core of the city (which was most often the same as the commercial heart of the city). It was not included in dictionaries as late as the 1880s. By the early 1900s, downtown was clearly established as the proper term in American English for a city's central business district.
The terms downtown and uptown can refer to cardinal directions, for example, in Manhattan, where downtown is also a relative geographical term. Anything south of where the speaker is currently standing, in most places, is said to be downtown. Anything north of the speaker is uptown. In the common New York phrase, "We're going to take the subway downtown," downtown refers to traveling in the geographic direction of south. A person standing on 121st Street and walking ten blocks south could also be said to have walked ten blocks downtown. The term uptown is used to refer to the cardinal direction north.
Such concepts derive from Manhattan's elongated shape, running roughly north/south and nowhere more than two miles (3300 meters) wide. As such, most of the train service and major thoroughfares on the island travel in the uptown/downtown directions. The other boroughs are wider, and "downtown" there refers to Lower Manhattan, Downtown Brooklyn, or some more local business district. Mercantile efforts to promote the South Bronx as "Downtown Bronx" have met little success.
Manhattan exceptions to the equation of "downtown" with "south" include Cherry Street and nearby parts of the Lower East Side, where downtown is westward towards City Hall, while south on Montgomery Street is not called downtown since it runs into the East River.
In New Orleans, "downtown" is a synonym for "downriver" and "uptown" a synonym for "upriver". The New Orleans central business district is referred to as "the CBD" rather than as "downtown".
In most other North American cities, "downtown" is the formal name of the neighborhood in which the city's central business district is located. Someone or something within the boundaries of that neighborhood is said to be "in downtown" rather than "downtown".