Answer:
Positive reinforcement is when you reward someone (person, child, pet, etc.) when they do what you want them to, and you ignore them when they do what you don't want them to do. Negative reinforcement, I believe, is when you punish someone for doing what you don't want them to do.
As far as their effectiveness, it seems that a combination of both is good. Positive reinforcement is essential, and negative reinforcement helps to round it out. It is, however, important to be careful with negative reinforcement because if you put too much attention on someone while trying to enact the punishment (IE, time out), then, subconsciously, they may enjoy even the negative attention and thus you will have a counterproductive effect.