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Meep implements the finite-difference time-domain (FDTD) method for computational electromagnetism. This is a widely used technique in which space is divided into a discrete grid and then the fields are evolved in time using discrete time steps. As the grid and the time steps are made finer and finer, this becomes a closer and closer approximation for the true continuous equations, and one can simulate many practical problems essentially exactly. Though many quantities can be calculated, major applications include transmission and reflection spectra, resonant modes and frequencies, and field pattern.
For detailed description and tutorials, please refer to: http://ab-initio.mit.edu/wiki/index.php/Meep