A box model is a highly simplified representation of the ocean that typically divides it into two vertical layers. Usually these represent surface, seasonally-mixed waters (or the euphotic zone) and the deep ocean, with communication between them parameterised as a simple mixing rate.
For specific applications box models may have enhanced vertical resolution (e.g. the carbon model; see diagram to the right) or add a degree of horizontal complexity (e.g. separate ocean basins or regions).