This program models one-dimensional cellular automata. A cellular automaton is a computational machine that performs actions based on certain rules. It can be thought of as a "board" which is divided into cells (such as the square cells of a checkerboard). Each cell can be either on or off. This is called the "state" of the cell. According to specified rules, each cell will be on (alive) or off (dead) at the next time step. In this case of one-dimensional cellular automata, each cell checks the state of itself and its neighbors to the left and right, and then sets the cell below itself to either on or off, depending upon the rule. This is done in parallel and continues until the bottom of the board.
For detailed instructions on using the program, take a look at the info window from the Cellular Automata model.
Click on one of the pictures to see a quicktime movie of the model: