Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.
The finite difference method is a numerical method for solving differential equations. The derivatives are discretized in space and in time and approximated by "finite differences" (derived from Taylor's Theorem) e.g.: $$ f^{'}(x) = \frac{f(x+h) - f(x)}{h} $$
where h is the distance between discrete grid locations.
The finite difference method can be solved using either explicit or implicit methods. For a more complete description see the Wikipedia page on the Finite difference method
