The dictionary definition of red light district is the area of a town or city in which one would find brothels (whether by custom or ordinance in the areas that such things are legal). But I thought I had seen references to it that predate traffic lights; help arrives from http://www.notfrisco.com/prisonhistory/glossary/glossR.html:
The term...was said to have originated in Dodge City, Kansas. Dodge City was a major stop for the railroad, and a convenient place for the train crews to visit ladies of negotiable virtue. When these men entered the brothels, as they often did, they would leave their red lanterns outside so they could be located in case of an emergency. The madams soon realized that a red light was an excellent way to advertise, and the custom spread. The red light in front of a place of prostitution eventually became a law, and every brothel and crib had to display the light during the night. Many cities also insisted that a red shade or curtain be hung in the windows of these establishments during the day. Seagraves 1994: 28
Snopes has an article about this theory, but they have been unable to verify it. In any case, though, mentions of it do predate the traffic situations found in modern cities, and tend to relate to a house having red lights.
Indeed, if one is reading a book where a house of ill repute appears, it may have red lights outside. Because of this, I used to think that everyone (well, at least members of the dominant American culture) knew what red lights outside a house signified.
I was riding in a pickup truck with two of my fraternity brothers one December night, and we passed a house whose Christmas lighting scheme was purely red light based. As a joke, I quipped, "Guess we know what in-home business they have!" Silence greeted me, followed by a "What do you mean?"
"They have red lights -- it means that it's a brothel, at least in theory," I said.
"That's weird. Must be another odd thing about your hometown." It occurred to me that they were both country boys. When we were all drinking later, they retold the story to everyone present and discovered that I was not pulling their leg.