A General Circulation Model (GCM) is a mathematical climate model of the general circulation of a planet's Atmosphere or ocean. It incorporates fluid dynamics (Navier-Stokes Equations), rotation, and Thermodynamics. Such a model can be analytic or can be fleshed out with computer-based Numerical simulations.
Such models have been developed for the Earth, but also adapted to other planets and Moons. With the study of Extra-Solar Planets, there is much opportunity for using them.
GCM can also stand for Global Climate Model, and detailed Global Climate Models can be General Circulation Models.