A globe is more accurate than a flat map because it mimics the true shape of the Earth and is able to accurately portray continent shapes and distance between landmasses. A map, which attempts to create a flat rendering of a round planet, distorts continent shapes and sizes.
Early astronomers believed that the world was a flat disc surrounded by water. This theory was eventually disproved by several occurrences, such as the rising and setting of the sun and the circular movements of stars in the sky. Around 250 B.C., Greek mathematician Eratosthenes approximated the diameter of the Earth. Though his calculations were slightly inaccurate, they bolstered the theory that the Earth was round.
A Greek named Crates of Mallus constructed the first globe around 140 B.C. This globe would have been highly inaccurate, as the Greeks only knew what some of the Earth looked like. Chinese astronomers living in this era assumed that the Earth was the round yolk of an egg-shaped universe. There was also a small group of Chinese astronomers who assumed that the universe was infinite, with planets and stars floating around great distances apart from each other. This theory, though the closest to the truth, was eventually abandoned in favor of the "egg universe" theory.
There were several other theories about the shape and motion of planets within the universe over the centuries. Isaac Newton was the first to come up with a theory that explained the movements of the stars, the sun, the moon and the planets.