a row or grid of cells in which each cell has an initial value and all cells are simultaneously evaluated and updated according to their values and the values of their neighbors.
A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired."
-Source: Wolfram Mathworld.
Also see the Wikipedia page on Cellular Automata.