Atoms are tiny particles that make up the universe, while molecules are made from atoms (even a single atom). However, both constitute small, identifiable units.
Atoms are what make up everything from pencils to humans to the ocean. At one time, scientists thought they were the smallest possible particle and that they were indivisible; however, they can be divided. Each atom has a nucleus made of protons and neutrons surrounded by orbiting electrons. Protons are positively charged, and electrons are negatively charged. Neutrons are neutral. All three of these particles can be divided up into smaller particles called quarks. The number of protons, neutrons and electrons an atom has determines what element it is. For instance, sodium has 11 protons, 11 electrons, and 12 neutrons.
A molecule, on the other hand, is indivisible in its own way: by definition, it is the smallest particle of a substance that still retains the properties of that substance. Therefore, although it can be divided into smaller parts (atoms and so on), it does make a unit. Single atoms can make up a molecule, such as the noble gases.
Most molecules are formed when atoms bond in a particular way. For instance, the chemical formula for water is H20, meaning that two hydrogen atoms bond with one oxygen atom. One set of this compound, exactly two hydrogen atoms and one oxygen atom, makes a molecule. If it were divided again, it would be hydrogen and oxygen atoms, not water.