Since atomic nuclei are very stable, the protons and neutrons must be kept inside them by some force and this force must be rather strong. What is this force? All of modern particle physics was discovered in the effort to understand this force!
Trying to answer this question, at the beginning of the twentieth century, physicists found that all they knew before, was inadequate to explain how the nucleus held together in spite of the electrostatic repulsion of the protons pushing it apart. They knew only gravitational and electromagnetic forces. It was clear that the forces holding nucleons were not electromagnetic. Indeed, the protons, being positively charged, repel each other and all nuclei would decay in a split of a second if some other forces would not hold them together. On the other hand, it was also clear that they were not gravitational, which would be too weak for the task.
The simple conclusion was that nucleons are able to attract each other by yet unknown nuclear forces, which are stronger than the electromagnetic ones. Further studies proved that this hypothesis was correct.
Nuclear force has rather unusual properties. Firstly, it is charge independent. This means that in all pairs , , and nuclear forces are the same.
Secondly, at distances of about meter, the nuclear force is attractive and very strong, roughly 100 times stronger than electromagnetic repulsion.
Thirdly, the nuclear force is of a very short range. If the nucleons move away from each other for more than few fermi (1 fermi = 1 fm [femtometer] = meter) the nuclear attraction practically disappears. Therefore the nuclear force looks like a strong man with very short arms.