An atom is the smallest piece of an element which still has the element's chemical properties. They are made up of smaller particles called protons, neutrons and electrons. The protons and neutrons bond together in the middle to form the nucleus and the electrons rotate around this nucleus in a cloud. The ratio of protons to neutrons is unique to one sort of atom. An element is lots of atoms, but they all contain the same amount of protons to neutrons. If two sorts of atoms combined, a compound would be created. Some different sorts of atoms are glad to bond together and form molecules (oxygen + chlorine), but others do not bond very well (neon + argon).
A molecule is made up of at least two atoms held together with very strong chemical bonds. These bonds are made because of the constant passing of electrons between atoms. A molecule is the smallest particle, next to atoms, in a chemical compound or element that actually has the chemical properties of that compound or element.
If you find this hard to understand, visualise a pile of paper clips which are all the same. They all have the same colour, size, and weight. If you divide your pile into two separate equal piles, and divide those piles in two, eventually, you will have one paper clip per pile. These can represent an atom. Your paperclip is still useable (i.e. it still has it's chemical properties), but if you divide even more by cutting the paper clips in half, they won't be able to actually hold paper. Now visualise a different pile of paper clips, but they are all still the same. Separate them down like the first pile and you get your atoms. Then take a paper clip from each pile and clip them in together. You have now created a molecule, i.e. two atoms joined chemically. The full pile of all the same paper clips (atoms) would represent an element.