Take for example the combustion of methane (#"CH"_4"#):
#"CH"_4"# + #"O"_2"##rarr##"CO"_2"# + #"H"_2"O"#
If you count the number of atoms (subscripts) of carbon, hydrogen, and oxygen on both sides of the equation, you will see that on the reactant side (left side), there are one atom of carbon, four atoms of hydrogen, and two atoms of oxygen.
On the product side (right side), there are one atom of carbon, two atoms of hydrogen, and three atoms of oxygen. Therefore, the equation does not satisfy the law of conservation of mass, and is not balanced.
In order to balance the equation, we must change the amounts of the reactants and products, as necessary, by adding coefficients in front of the appropriate formula(s).
When balancing an equation, NEVER change the subscripts, because that changes the substance. #"H"_2"O"# is NOT the same substance as #"H"_2"O"_2"#. To determine the number of atoms of each element, the coefficient is multiplied times the subscripts in each formula. If there is no coefficient or subscript, it is understood to be 1. The balanced equation for the combustion of methane is:
If you compare the unbalanced equation to the balanced equation, you will see that the chemical formulas of each reactant and product were not changed.
The only change is the coefficient of 2 written in front of the formula for oxygen on the reactant side, and the coefficient of 2 written in front of the formula for water on the product side.
So now there are one carbon atom, four hydrogen atoms, and four oxygen atoms on both sides of the equation, and the equation is balanced. Now the equation says that "One molecule of methane plus two molecules of oxygen produce one molecule of carbon dioxide and two molecules of water".
When working with moles, the equation would be read as "One mole of methane plus two moles of oxygen produce one mole of carbon dioxide and two moles of water".
Here is a video which discusses the importance of balancing a chemical equation.