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The definition of atom is: a unit of matter that is the smallest unit of an element, having all the characteristics of that element and consisting of a dense, central, positively charged nucleus surrounded by a system of electrons. The entire structure has an approximate diameter of 10-8 centimeters and characteristically remains undivided in chemical reactions except for limited removal, transfer, or exchange of certain electrons. It is the smallest possible part of an element that still remains the element.
Under normal circumstances an atom can not be broken down into any particles smaller than an atom, but we humans, have devised ways to break the atom apart. That is the entire basis of the atom bomb, particle colliders, and quarks. It takes high speed, high energy smashing of particles to break an atom. A particle collider does that and helps us understand some of the theories in particle physics. The results of an atom bomb are widely known. Quarks are extremely small particles that do not exist alone. They must group to form the protons, electron, and neutrons normally found in a single atom of an element.
An atom itself is made up of three kinds of subatomic particles: protons, neutrons, and electrons. The protons and the neutrons make up the center of the atom called the nucleus and the electrons fly around above the nucleus in a small cloud. The electrons carry a negative charge and the protons carry a positive charge. In a neutral atom the number of protons and the number of electrons are equal. Often, but not always, the number of neutrons is the same, too. The opposing forces attract and repel each other so as to keep the atom together.
Here on Universe Today we have a couple of great articles about atoms: one is about atomic radius and the other is about the most widely accepted atomic model. Astronomy Cast offers an episode about how atoms act in space.
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