Strong nuclear force” is a somewhat old-fashioned term for the “strong interaction”, which is the interaction between quarks that make up a nucleus. This force is very short range, but in that short range, stronger than any of the other forces of nature, hence the name.
The strong nuclear force is the force that holds protons and neutrons together. It also holds them all together in a nucleus and is responsible for the energy released in nuclear reactions, except for a much smaller portion due to the weak force, which is involved in beta decay.