What is the purpose of the giants game. What do the rules appear to be, and how does ender finally get past this part of the mind game ?

The purpose of the Giant's game was to create a no-win situation to force Ender to think outside of the box. Finally, Ender kicks over the two glasses, jumps into the Giant's face, and digs into the Giant's eye. Eventually, the Giant falls over dead, and Ender reaches Fairyland.