Nuclear binding energy is the energy needed to break an atomic nucleus into protons and neutrons. Atoms with higher binding energy are more stable, because you would have to add more energy to break them.
Protons and neutrons are attracted to each other by the nuclear force. This is a form of the strong interaction that acts over a longer distance than usual. Together, protons and neutrons are called nucleons.
The binding energy per nucleon is the binding energy of an atom, divided by its number of protons and neutrons. Iron-56 has the highest binding energy per nucleon. This makes it the most stable isotope of any element. Both smaller and larger atoms may eventually move towards Iron-56 by gaining or losing nucleons.
The term nuclear binding energy can be confusing. An atom with a higher nuclear binding energy does not have more energy stored in its nucleus. Actually, atoms with more binding energy have less energy stored inside.