Positive reinforcement is when you strengthen a behavior by adding something to it.
For instance if Jenny cleaned her room and I complimented her work.
Positive Punishment is the presentation of a stimulus(usually an unpleasant one) following a response that leads to a decrease in the future strength of that response.
Don't do your homework, and you get an incomplete grade.
Negative reinforcement is when you take away a stimulus(usually an unpleasant one) following a response, which leads to an increase in the future strength of that response.
Drive safely and your car insurance rates go down.
Negative punishment consists of the removal of a stimulus (one that is usually pleasant) following a response, which then leads to a decrease in the future behavior.
Won't share toys then your parents take your toys.
This is a good video.
When using the four contingencies above it is very important to use the proper one in the proper circumstance. I have 2 kids and if all you do is threaten to take things away or spank them then they will not be very happy in the long term. You don't have to spoil them, but sometimes a good compliment or playing a game is a good positive reinforcement tool.