This is a phenomenological potential and the string part is not, as yet, derivable from the fundamental theory of QCD, although numerical calculations and plausibility arguments suggest that QCD is in agreement with the observations. This binding energies can be approximately understood as the sum of several terms. It takes energy to force protons together into a nucleus.
Nuclear forces are short range.
Nucleons at the surface are not surrounded by other nucleons so they should have less nuclear binding energy. If the nuclear forces are nearest neighbour forces, then the this surface contribution to the binding energy should just be proportional to the number of surface nucleons. As you add nucleons to a nucleus, the nucleons must go into higher and higher energy states, with one neutron and one proton allowed to share each quantum state. Thus the Pauli exclusion principle favours nuclei with equal numbers of neutrons and protons. It must be remembered that this formula is only approximate.