The Law of Conservation of Mass tells us that in an isolated system (the chemical reaction in this case), mass is neither created or destroyed. Furthermore, the mass of the reactants must be equal to the mass of the products. Chemical equations must always be balanced in that exactly how many atoms you used of each element in the reaction will make up the result. For example, the formation of water:
2H₂ + O₂ → 2H₂O
On each side we have 2 hydrogen atoms and 2 oxygen atoms. Thus, the mass on each side is the same. The elements have simply rearranged to form new compounds.