It turns out that some particles (quarks and gluons) have a type of charge that isn't electromagnetic; rather, it is called color charge. The force between color-charged particles is very strong, earning it the name Strong Force.
It is important to note that only quarks and gluons have color charge. Hadrons (such as protons and neutrons) are color neutral, as are leptons. For this reason, the strong force only acts on the really small level of quark interactions.