This is John Conway's "Game of Life" cellular automaton model. Each site in the grid is either dead (black) or alive (green). On every time step, each site looks at its 8 neighbors (including the diagonal neighbors). If a site is alive, it will stay alive if it has 2 or 3 live neighbors; otherwise, it dies from loneliness or overcrowding. If a site is dead, it will become alive if exactly three of its neighbors are currently alive.
That's it! The behavior of each site in the grid is very simple, but the behavior of the whole system is very complex. You can often see "gliders", small patterns of live cells which move diagonally across the grid. (Note that the sites themselves don't move; it's the pattern of information which moves.)
"Life" is really quite amazing --- it has been shown to be "computationally universal", which basically means that it is possible embed arbitrarily complex calculations into the simulation. Basically, it's possible "draw" a computer which performs actual calculations!
See the parent web page for general controls.
Controls specific to this particular applet does not have any specialized controls yet. Hopefully some generalizations will be added later on.