Consider the earth and a rocket ship which are bound together by gravity. If it takes work or energy to pull them apart, then the binding energy is the amount of energy it takes to completely separate them. Similarly the binding energy in a nucleus is the amount of energy it takes to completely separate the protons and neutrons, (collectively called nucleons.)
There are two forces acting inside the nucleus of atoms. The nuclear force -- a residuum of the strong force that holds quarks together -- is pulling the neutrons and protons together -- and the electric charge on the protons is pushing them apart. The strong force is a lot stronger than the electric force at short ranges up to two and a half times the proton diameter, but at larger distances the electric force dominates.
This increase in binding energy continues until we get to iron and nickel where the nucleus has about 60 nucleons in it. At this point, the nucleus has a radius more than two and a half nucleons wide, which you remember is the range at which the repulsive ElectroMagnetic Force begins to dominate.. . So as we add nucleons past this point the electric force trying to tear the nucleus apart starts winning and each added nucleon is a little less-tightly bound.
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