Step 1: Picture atoms as building blocks that cannot vanish.
In any chemical reaction, atoms are simply rearranged into new combinations, none of them are created out of nothing and none of them disappear.
Step 2: See what this means for a written equation.
If a reaction starts with a certain number of atoms of each element, the products must end up with that exact same number of atoms of each element too, since nothing was lost along the way.
Step 3: Connect this to balancing.
Balancing an equation is just the bookkeeping step where we adjust coefficients until the atom count on the reactant side exactly equals the atom count on the product side.
Step 4: Name the underlying law.
This atom counting requirement is a direct expression of Lavoisier's law that mass is neither created nor destroyed in a chemical change. \[ \boxed{\text{Law of conservation of mass}} \]