In 1956, Samuel Shelton founded a society that subscribed to a theory about the shape of the Earth -- namely, that it's flat. Shelton based his theory upon what he called common sense and personal observation. He called the scientific evidence for a globe-shaped Earth "dogmatic," meaning scientists were making this claim without adequate evidence. Later, when people showed him pictures of the Earth taken by satellites, Shelton claimed the photos were fake. He and the members of his society continued to support the idea that the Earth is flat and that those who disagree are part of a conspiracy to keep the truth about the Earth hidden.
Shelton died in 1971, and leadership of the society passed to Charles Johnson. Johnson led the society until his death in 2001. Without leadership, the society fell apart. Critics of the Flat Earth Society say that its members simply deny any evidence that conflicts with their world view without offering real alternative hypotheses.
Keep in mind that humans have known Earth was round for centuries. The ancient Greeks learned by measuring shadows that the planet's surface must be curved. That led to astronomers concluding that the world was round. The myth that people during Christopher Columbus's journeys believed Earth to be flat has no real basis in fact -- the argument was really about how big Earth was, not whether or not it was flat.