Atomism was one of the theories the ancient Greek natural philosophers devised to explain the universe. The atoms, from the Greek for "not cut" were indivisible. They had few innate properties (size, shape, order, and position) and could hit each other in the void. By hitting one another and locking together, they become something else. This philosophy explained the material of the universe and is called a materialist philosophy. Atomists also developed ethics, epistemology, and political philosophy based on atomism.
Leucippus and Democritus:
Leucippus (c. 480 - c. 420 B.C.) is credited with coming up with atomism, although sometimes this credit is extended equally to Democritus of Abdera, the other main early atomist. Another (earlier) candidate is Moschus of Sidon, from the Trojan War era. Leucippus and Democritus (460-370 B.C.) posited that the natural world is comprised of only two, indivisible bodies, the void and atoms. Atoms continually bounce around in the void, bouncing into each other, but eventually bouncing off. This movement explains how things change.
Motivation for Atomism:
Aristotle (384-322 B.C.) wrote that the idea of indivisible bodies came in response to the teaching of another Pre-Socratic philosopher, Parmenides, who said that the very fact of change implies that something that is not either really is or comes into being from nothing. The atomists are also thought to have been countering the paradoxes of Zeno, who argued that if objects can be infinitely divided, then motion should be impossible because otherwise a body would have to cover an infinite number of spaces in a finite amount of time.
The atomists believed we see objects because a film of atoms drops off the surface of the objects we see. Color is produced by the position of these atoms. Early atomists thought perceptions exist "by convention," while atoms and the void exist by reality. Later atomists rejected this distinction.
A few hundred years after Democritus, the Hellenistic era revived the atomist philosophy. Epicureans (341-270 B.C.) formed a community applying atomism to a philosophy of living a pleasant life. Their community included women and some women raised children there. Epicureans sought pleasure by getting rid of things like fear. Fear of gods and death are inconsistent with atomism and if we can get rid of them, we will be free of mental anguish.
Source: Berryman, Sylvia, "Ancient Atomism", The Stanford Encyclopedia of Philosophy (Winter 2005 Edition), Edward N. Zalta (ed.)