After divorce, whoever has custody gets paid child support. The mother is awarded custody in most cases, unless there's some compelling legal reason not to. So the father usually ends up paying support. The amount has to do with many factors, including how much each parent makes. If there's a big difference between incomes, the one who makes more ends up footing almost the full cost of raising the child.
Think of the parents' combined monthly income as a pie. When they were married, the dad put in 8 slices and the mom put in 4. Every month, they take out 4 slices to pay for the kids' clothes, school, food, child care, and their portion of the household expenses (rent, electric, heat, etc.).
So after the divorce, the dad takes his 8 slices away but leaves the kids behind in the house with the mom, who's only earning 4 slices a month. She can't very well use all 4 slices to pay for the kids, because she needs almost all of that just to care for her own expenses. So the divorce settlement will require dad to pay 3 and 1/2 slices a month, and the mom will have to come up with the other 1/2 slice on her own. Make sense?