How are coefficients used to balance chemical equations?

According to the law of conservation of mass, the quantity of the elements, involved in chemical reactions does not change. For example,

H2O2 - > H2O + O2

is wrong, because there are two O atoms on the first side of the equation, and three on the other. To correct it, coefficients must be added, until the amount of both H and O atoms is equal on both sides.

2H2O2 - > 2H2O + O2