The strong nuclear force is indeed the strongest of the Four Forces of Nature, but it only works at the heart of the atom and has a very small range, just 10-16 metres. This range is only just bigger than a proton or neutron and it comes from the gluons that hold the innards of the proton and neutron together.
A nucleon (i.e. a single proton or neutron) is made up of quarks, three in total, and they are the most fundamental particles know to science today. That is not to say that quarks cannot be broken down into smaller pieces but we cannot make anything smaller than quarks in particle colliders using current technology. There are six types of quarks, up, down, strange, charm, top and bottom, but it is only the up and down that make up nucleons; the others are produced in particle colliders but quickly decay into up and down quarks.
Gluons come in different colours, red green and blue as well as their opposites anti-red, anti-green and anti-blue. Like colours repel and unlike colours attract. The use of the term colour here is used just to distinguish different gluons apart. They are not actually coloured and do not emit light at all. It is the gluons that are generate the strong force and you can think of them “gluing” the individual quarks together inside each nucleon. A little bit of this strong force overflows and “glues” the individual nucleons together in the heart of the atom. This force has to be strong so that it can overcome the repulsive electromagnetic force experienced by two protons in the same atom. Indeed the strong force is so strong that it is 100 times stronger than the electromagnetic force. But the strange part of the strong force is that as the atom gets bigger by adding more nucleons the strength of the strong force decreases rather than increases.
As the strong force has such a short range it takes a lot of energy (temperature) and pressure to get two nucleons close enough to overcome the electromagnetic force. Such places occur deep in the heart of stars and also when a star dies in a massive supernovae.
The strong force is responsible for creating nucleons and for holding them together in atoms. Without this fundamental force none of us would be here today and the universe would probably not exist! Extraordinary.
Important!Information taken from Universe, 9th edition, Freedman et al, 2011, ISBN-10: 1-4292-3153-X