A binding energy is generally the energy required to disassemble a whole system into separate parts. It is known the sum of separate parts has typically a higher potential energy than a bound system, therefore the bound system is more stable. A creation of bound system is often accompanied by subsequent energy release. We usually distinguish the binding energy according to these levels:
At atomic level the atomic binding energy of the atom derives from electromagnetic interaction of electrons in the atomic cloud and nucleons (protons) in the nucleus. The atomic binding energy is the energy required to disassemble an atom into free electrons and a nucleus. This is more commonly known as ionization energy.
At molecular level the molecular binding energy of the molecule derives from bond-dissociation energy of atoms in a chemical bond.
At nuclear level the nuclear binding energy is the energy required to disassemble (to overcome the strong nuclear force) a nucleus of an atom into its component parts (protons and neutrons).