Your Conscience is something in your head that distinguishes right from wrong. When you make a decision, the voice that's in your head is Your Conscience, and is the little bitch that makes all the bad descisions in your life, but also the angel that completely prevents an apocalypse or whatever.
Your Conscience has a split personality, and often takes the form of an "angel" or a "devil." It's kind of creepy because only you can see them. The little dudes sometimes look like you, either in a white dress or completely red with purple horns. Creepy, huh?