What is the difference between atoms and elements?
Get ready for an imperfect analogy.
Imagine going to an ice cream store. Let's say they have 30 different flavors of ice cream. Those are elements, the things I have available from which to build my dessert. The smallest amount of ice cream the store will sell to me is a scoop. This is an atom. If I want, I can put two or more scoops of ice cream together. This is a molecule. If my molecule has more than one flavor of ice cream, I can call it a compound.
So, in summary:
element - a basic substance that can't be simplified (hydrogen, oxygen, gold, etc...)
atom - the smallest amount of an element
molecule - two or more atoms that are chemically joined together (H2, O2, H2O, C6H12O6, etc...)
compound - a substance that contains more than one element (H2O, C6H12O6, etc...)
What's wrong with the ice cream analogy? Splitting an atom creates different elements (split an oxygen atom and you don't have oxygen any longer). Splitting a scoop of ice cream results in smaller blobs of the same flavor. For the analogy to hold true, the flavor of the ice cream would have to change when you split a scoop (the chocolate 'element' would have to change into some other 'element' (flavor)).
Also, what constitutes a molecule isn't quite as clean-cut as it's stated here. Atoms can bond by sharing electrons (a molecular bond) or by completely transferring electrons from one atom to another (an ionic bond). Properly, only something with molecular bonds can be called a molecule. We very cleverly avoided listing any ionic compounds (such as NaCl) in our molecular example list for this reason.