Quantum Chromodynamics (QCD) is the quantum field theory of the strong force, which is the force that holds the nucleus of an atom together. The strong force exists between the quarks and gluons that make up hadrons; examples of hadrons are the protons and neutrons of a nucleus, as well as pions, etc. The gluons are the messenger particles that carry the force of the strong interaction between the quarks in a hadron.
QCD, like quantum electrodynamics (QED), is a part of the Standard Model of physics. In QED there is only one type of charge (electrical), but in QCD there are three: they are called the color charge, and are named red, green and blue. The strong nuclear interaction is therefore sometimes referred to as the color force.
QCD is thought to contain a property called quark confinement, where quarks that are separated do not have a diminished force between them. QCD also has the property of asymptotic freedom, where at high energies, quarks and gluons interact only weakly. Because of quark confinement, it would take an infinite amount of energy to separate two quarks.
Quark confinement is not analytically proven, but it is believed to be the explanation for the lack of observation of free quarks. The concept of quark confinement is supported by lattice QCD computations. One of the Millennium problems that carry a large prize is to prove quark confinement mathematically.
Each of the Standard Model theories uses gauge theory, which means that a change of scale, or gauge, creates a local or global symmetry of the theory. QCD is a non-Abelian gauge theory, which contain the feature of asymptotic freedom. Non-Abelian gauge groups are gauge grooups that are not commutative. The non-Abelian gauge group of QCD is SU(3), which is able to describe the three color charges of the strong force. In contrast, QED has the Abelian gauge group U(1). In QCD, there are 8 gauge fields, corresponding to the 8 different types of gluons.
Lattice QCD is the theory of QCD on a spacetime lattice. The reason lattice QCD is needed is because the strong force is very nonlinear; this makes analytic or perturbative solutions in QCD hard. A spacetime lattice makes spacetime effectively discrete instead of continuous; there is therefore a momentum cutoff on the order of the inverse of the lattice spacing; this regularizes the theory. Lattice QCD is used to investigate quark confinement and quark-gluon plasmas.