What is the fundamental force which holds particles together to form protons and neutrons?

It is called the Strong Force, specifically the ResidualStrong Force. The Fundamental Strong Force is what holds quarks (which make up Protons and Neutrons) together. The Residual Strong Force is mediated by virtual mesons and has an effective range of 10^(-15) Meters and gets significatly weaker beyond this point. This is the diameter of a Lead atom's nucleus- any bigger and it will become unstable, which is why all elements greater than this are radioactive.