The Game of Life is a cellular automaton, which means that it consists of a grid of cells which can be in one of a finite number of states. Given any state, there are rules that govern what the next state of the grid will be.
Each cell in a grid can be either dead or alive. To find the next state of the grid, the following rules are observed:
Any living cell with 0 or 1 neighbours dies, as if by underpopulation
Any living cell with 4 or more neighbours dies, as if by overpopulation
Any living cell with 2 or 3 neighbours survives, yay
Any dead cell with 3 or more neighbours becomes alive, as if by reproduction
You can make some pretty cool patterns just by doodling all over the grid and hitting \'Go\'. Or there are some examples all over the net of clever states. Try importing Gosper\'s Glider Gun: