The System is a giant glowing white cube (called God cube in the achievements) with a sort of sophisticated armor around.
It seems like it gets closer to the player's cube as he progresses trough the game, both in game and in the cinematics scenes.
It talks to the player at the beginning of each section to congratulate the Kube, or introduce new features when player unlocks them.
It tells us a little bit of its own story as it's trying to identify if you are a program or a human.