When molecules react with one another, atoms can't be created or destroyed. When atoms combine to form different molecules during a chemical reaction, they can be represented by a balanced chemical equation.
There must be the same number of each element at the beginning and end of the chemical reaction.
Hydrogen and oxygen react to form water:
H2 + O2 ----> H2O
On the left side of the reaction arrow (---->) there is 2 hydrogen atoms and 2 oxygen atoms. On the right side of the reaction arrow (---->) there are two hydrogen atoms and one oxygen atom. The chemical equation is not balanced because there is one less oxygen on the right side of the reaction arrow than there are on the left -- remember, atoms cannot be created or destroyed and there needs to be an equal number of atoms on both sides of the reaction arrow.
Coefficients are used to represent the number of each molecule being used in a reaction. In this example, the coefficients balance the chemical reaction by insuring that there are the same number of atoms at the start and end of the reaction.
With the coefficients added to the chemical equation, there are 4 hydrogens and 2 oxygens at the beginning of the reaction and 4 hydrogens and 2 oxygens at the end of the reaction.
The coefficients produce a balanced chemical equation.