QCD is a well-estabilished mathematical model that describes quark and gluons, basic constuents of proton and neutrons and the majority of ordinary matter. QCD is a Quantum Field Theory, i.e. it belongs to a class of mathematical models which is a superset of both Quantum Mechanics and General Relativity. The basic degrees of freedom of QCD are fields which evolve according to the law of quantum physics. QCD is a part of the Standard Model of Particle Physics a unified framework derived in the 1960s from which all known laws of physics can be derived and the properties of all observed objects can be computed. The Standrad Model of Particle Physics depends on only 19 parameters that need to be measured (indirectly) by comparing experiments with model prediciton.
The goal of Lattice QCD is that of determining those parameters, specifically, the masses of quarks and the relative strenght of their interactions. This is achieved by simulating QCD in a computer where the space and time are discretived on a lattice and the quantum affects are realized by introducing a fifth dimension (simulation time) by means of a Markov Chain Monte Carlo.
Lattice QCD allows to compute propeties of composite particles from an input estimate of few fundamental parameters and those properties can then be compared with experiments to verify the assumptions.
To date the Standard Model and QCD have been successful at desrcibing physical phenomena from the scale of 10-18m and above (anything bigger than a billionth or a billionth of a meter). Yet it is expected that the model will eventually break when (if) smaller and smaller structures are discovered. Lattice QCD can play an important role in the potential discovery of these smaller structures and well as explaining their origin.
