Well, at first cinema owners wanted to keep it classy. You've probably seen pictures of the old "movie palaces" with rich carpets and fancy interiors. Cinema owners wanted the movie-going experience to have a similar gravitas as live theatre, and the last thing they wanted was people eating during a movie.
However, street vendors loved popcorn. It was dirt cheap: a 50 pound bag of popcorn only costs around $30 these days, and would last a vendor several months if stored properly. Popcorn doesn't require refrigeration like hot dogs or hamburgers, and doesn't need a lot of extras (unlike hot dogs, with their buns, ketchup, mustard, relish, napkins, etc.). Popcorn didn't require a lot of expertise to make, and it smelled great, enticing possible customers.
The first steam-powered portable popcorn cookers came out in 1884 [citation needed], and popcorn soon became a popular street snack. It didn't take long for vendors to make a connection with movies, as it used to be common for "movies" to last hours, with double features, cartoons, newsreels and such. People would naturally get hungry spending four hours at the movies, so vendors would set up outside cinemas. People would sneak in bags of the stuff.
A lot of cinemas took a big hit during the Great Depression. Although a movie ticket might only have cost 25ยข, that was a big deal to a lot of families. People started staying home instead of going to the movies. Remember, before the Depression, almost 70% of Americans went to the movies every week. From 1932-1934 that number dipped to 40%. That's a huge drop-off.
Cinema owners, once totally against people eating during films, became so desperate for money that they started allowing vendors to sell food in the lobby... for a cut of their profits of course (which is one of the definitions of a "concession", which is why they're called "concession stands"). Sales of popcorn and drinks are the main reasons many cinemas stayed in business during the Depression (indeed: there was a cinema chain in Dallas that opened concession stands in all but five of their theatres, the other five considered "too classy" to sell food; within a couple of years, the cinemas that sold food were making healthy profits, while the "classy" cinemas that didn't lost a considerable sum of money.
So... by the time World War II came around, many cinemas got smart and stopped renewing their contracts with local vendors. Why let some Joe Schmoe make money selling popcorn in your lobby when the cinema owners could make it themselves and keep ALL the money? World War II also solidified popcorn as the "official" snack of the movies thanks to sugar rationing. The Japanese cut off quite a few sugar providers, like the Philippines. But the U.S. had plenty of corn, so popcorn was more readily available than candy at concession stands.
hi! not discouraging other responses, but you may be interested in these earlier posts