An element is the purest form of a substance and cannot be further purified or broken into simpler forms (it is already in the simplest form). There are over a hundred different elements known to us and they have been tabulated in the periodic table. An atom is the smallest unit of matter. Atoms of the same kind combine together to form an element. In other words, an atom is a constituent of the element. An atom is composed of sub-atomic particles such as protons, neutrons and electrons. An element is only pure and non-divisible because it contains atoms of the same kind. Sometimes, slightly different atoms (containing the same number of protons, but different neutrons) may be there in an element, and we end up with an isotope of the element. 

So, in short, atoms are the fundamental unit of matter and combine to form an element, which is the simplest form of matter.

Hope this helps.