The rules are specified in the small grids at the right. There are 8 rules, one for each row of the small grids. For example, the first row says, if a square is light blue, and so are the squares on either side, make the corresponding square in the next row light blue. The second row says, if a square is light blue, and so is the square to its left, but the square to the right is blue, make the corresponding square in the next row blue.
You can change the rules by clicking on the squares in the column on the far right, which will change their color. Since these squares determine what color the squares in the next row will be, these changes will affect the pattern. Try it: click some of the these squares, and press the random button. What different patterns can you create?
You can also experiment by controlling the color of the squares in the top row of the large grid. Click on these squares to change their colors, then press the generate button.
Reference: Wolfram, S. (2002) A New Kind of Science. Champaign, IL: Wolfram Media, Ch. 2.