Square dances were first documented in 17th-century England but were also quite common in France and throughout Europe. They came to North America with the European settlers and have undergone considerable development there.
The square dance is an American institution. It began in New England when the first settlers and the immigrant groups that followed, brought with them their various national dances, which we now call folk dances, but which were the popular dances of the day in the countries of their origin – the schottische, the quadrille, the jigs and reels and the minuet, to name a few. After a week of toil in building new homes and carving homes out of virgin forest, the settlers would gather in the community center on Saturday evening and enjoy dancing their old-world favorites. As the communities grew and people of different backgrounds intermingled, so did their dances. As the repertoire increased, it became increasingly difficult for the average person to remember the various movements.
In almost any group, however, there would be at least one extrovert, the hail-fellow-well-met, the life-of-the-party type, with a knack for remembering the dance figures. With typical Yankee ingenuity, the settlers let this person cue or prompt them in case they happened to forget what came next. In due course, the prompter (or figure caller, as he became known) acquired a repertoire of various colorful sayings or patter that he could intersperse with the cues. Quite often he would learn the dances of other communities and he would teach them to the group. Some of these men were quite ingenious and developed dances and routines of their own, including dances for groups of four couples. This is the manner in which square dancing and its director (or caller) developed.
I found this video on the American Square Dance