What are some examples of strong nuclear force?

The strong nuclear force binds protons and neutrons together to form atomic nuclei heavier than Hydrogen. It works in terms of binding energy which is also known as mass deficit. For example a Helium-4 nucleus has two protons and two neutrons. The mass of the Helium-4 nucleus is less that the masses of two free protons and two free neutrons.

Actually the strong nuclear force isn't a fundamental force. It is a residual effect of the colour force which binds quarks to make protons and neutrons. The colour force can bind a quark in a proton with a quark in an adjacent neutron. This is the strong force.

The strong force also explains how the Sun fuses Hydrogen into Helium. Protons are positively charged and repel each other. At the temperatures and pressures in the Sun's core, two protons can get close enough that the strong force overcomes the electrostatic repulsion and binds two protons into highly unstable Helium-2. Occasionally one of the protons decays into a neutron forming Deuterium. Further reactions take place until Helium-4 is produced and the binding energy is released.

The strong force is very short ranged and can only bind adjacent protons and neutrons. The electromagnetic force is long ranged which means that every proton in a nucleus repels every other one. This explains why all very heavy elements are unstable. The strong force isn't strong enough to overcome the electrostatic repulsion.