Read this. It helped me out A LOT!
http://www.embedded.com/2000/0010/0010feat3.htm
In math, function line is whatever is on your graph in the present, the derivative is the slope of a line at any point in time, and the integral is how much area fits under a curve in a given time range.
In robots, the present (P term) is where you are right now, the integral (I term) is where you have been, and the derivative (D term) is how fast you are getting to where you are going. If you know these three things, you can decrease the amount of time it takes to get to your set point, and decrease overshoot and settling time once you get there.
Doing control without the I and D terms is like driving a car with no rear view mirror or speedometer. Sure you know where you are on the road, but you have no idea when to speed up or apply the brakes.