Insulin and Glucagon are the two major hormones in the control of blood glucose, and although they have similar effects, they act in different conditions. When you eat a meal, Insulin is responsible for moving Glucose from the blood into the cells. Glucagon acts when the body needs to move Glucose form the blood into your cells from another source.
Before eating a meal, you are likely to have gone a while without eating, meaning the body needs to use the fuel you've stored away like Glycogen or Fat. Most important though is to keep the concentration of glucose in the blood incredibly constant, and Glucagon levels start to rise as time goes on without a meal to achieve this by breaking down Fat or Glycogen and put it in the blood as Glucose. As soon as you eat again, Glucagon levels drop and Insulin levels rise to use the food you've just eaten as fuel!