They worshiped a machine, Landru, created by their leader Landru circa 4286 BC, when war threatened to destroy all life on the planet. Landru created "the Body", similar to a hive mind. After the machine, Landru, was destroyed, a team of sociologists was left behind to give the culture a "more Human form". (TOS: "The Return of the Archons")
Background information Edit
This species was consistently described as being "Human" in the episode. This fits with the comic book The Return of the Archons, Part 2, where Beta III was revealed as a lost Federation colony.