Draw some patterns (communities of life) by clicking the left mouse button on squares to bring them to life.  Then click on the [Step] button to watch what happens as the rules are applied in one cycle of Life.  To repeat the cycle over and over forever, click on the [Go] button.

The Game of Life (invented by mathematician John Conway) is an example of Cellular Automaton.

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. (from http://mathworld.wolfram.com/CellularAutomaton.html).

The "Game of Life" plays out on a grid.  The squares of the grid are called cells.  A cell that is alive is colored in.  The rules for Life are simple.  They are:

1. In order for a cell to remain alive, it must have two or three neighbors.
2. If a live cell has less than two neighbors, it dies (loneliness).
3. If a live cell has more than three neighbors, it dies (over-crowdedness).
4. If an empty cell has exactly two neighbors, it comes to life.

A cell's neighbors are the eight cells which surround it (to its north, northeast, east, etc...).