From OpenFOAMWiki

This application solves the Laplace equation for unsteady, isotropic diffusion:

\frac{\partial T}{\partial t} - \nabla^2 \left( D_T \cdot T\right) = 0

where D_T is a constant. Since this application is one of the simplest possible OpenFOAM solvers, it is a useful starting point for understanding OpenFOAM solvers and the way they are programmed. The Doxygen version of the code can, for example, be found here (laplacianFoam.C for OpenFOAM 3.0). Since OpenFOAM use include files extensively it may be difficult to get the complete overview of the code in the beginning. The advantage is of course that writing new applications is simplified, since it is often sufficient to string together pre-programmed elements with minor modifications.