Quantum chromodynamics (QCD) is the theory that describes the interactions governed by the strong nuclear force. Where electromagnetism is mediated by the photon and the weak force by the W and Z bosons, the strong force is mediated by gluons. Gluons are force-carrying particles that hold quarks together and enable them to form the plethora of hadrons, such as protons and neutrons, that are known to exist.
The theory is described mathematically as a set of highly non-linear equations that are extremely difficult to solve without approximations. Approximations such as perturbation methods or lattice QCD techniques are extensively used to tackle problems in this domain.
A pair of properties that are unique to QCD help provide solutions to these problems: asymptotic freedom and confinement. Asymptotic freedom describes a phenomenon that is unlike most physical interactions; as the energy scale increases (i.e. separation distances get very small), quarks and gluons interact very weakly, allowing computations to be carried out for high energy interactions through perturbative methods.
Confinement, on the other hand, dictates that the force between two quarks does not decrease as their separation increases. If you pull two quarks apart, the potential energy between them will eventually become so great that a quark-antiquark pair will appear out of the vacuum to release the strain. While this has not been proven mathematically, it is believed that confinement is why no free quarks have ever been observed; they always exist bound in hadrons.