How can the law of conservation of mass be applied?
The more you eat, the fatter you get!
In simple classical systems it's so obvious that it really doesn't really have a particular role at all.
However, once we realise that mass is equivalent to energy and so there can be transformations between the two, then it becomes much more interesting. When a uranium nucleus undergoes fission, we find that the masses of the products do not add up to the original mass; the difference is released as (kinetic) energy:
An awful lot of energy!
The law of conservation of mass states that in a closed system, mass is neither created nor destroyed during a chemical or physical reaction. The law of conservation of mass is applied whenever you balance a chemical equation. It is also applicable to stoichiometry.