The grid can be in any finite number of dimensions. Time is also discrete, and the state of a cell at time t is a function of the state of a finite number of cells called the neighborhood at time t-1. These neighbors are a selection of cells relative to some specified, and does not change (Though the cell itself may be in its neighborhood, it is not usually considered a neighbor). Every cell has the same rule for updating, based on the values in this neighbourhood. Each time the rules are applied to the whole grid a new generation is produced.
applicable to Crypto Graphy?
http://cscs.umich.edu/~crshalizi/notebooks/cellular-automata.html - Each cell is a sort of very stupid computer - in the jargon, a finite-state automaton (Finite State Machine?) - and so the whole board is called a cellular automaton