Atomism is an idea in Metaphysics. It says that everything that can be touched is made of smaller things that are made of smaller things that are made of even smaller things but that eventually you get to something so small that nothing smaller can exist called an Atom. [source?]
History
The Greek philosopher Anaxagoras said that everything that can be touched is made of smaller things called “Seeds” and that there are many different kinds of “Seeds”. According to him, nothing can be a smaller than a “Seed” and what different objects are like is because of the different kinds of Seeds they have. Later, the philosopher Leucippus and his student Democritus said that everything that can be touched is made of smaller things that are made of even smaller things that are made of even smaller things. But Leucippus and Democritus also said there are things so small that nothing smaller can exist called Atomos Particles and that everything is made of them. Democritus said that there is empty space between all Atomos Particles. He also said that we call different groups of Atomos Particles different things (like Water, Fire, Earth and Air) but that Atoms and Space are the only things that really exist and everything else just looks like it exists.
Aristotle said that Democritus was wrong. He said everything you can touch is made of smaller things that are made of smaller things that are made of smaller things and that this goes on forever. According to him, there is no smallest thing. This is called the Continuous Theorem. Since then a lot of people debated if Aristotle were right or if Democritus were right. Then John Dalton came up with The Atomic Theory which said that all Matter was made of Atomos Particles called Atoms. And Dalton based that idea on Democritus.