The Law of Conservation of Mass simply states that matter cannot be created nor destroyed. The law was first introduced to the world by Antoine Laurent Lavoisier (1743-1794), the "Father of Modern Chemistry", by showing conservation of mass in chemical reactions.

The law can be taken further in that:
Mass of All Reactants = Mass of All Products;
Matter cannot be created from nothing, it can only change its form during chemical reactions.

See: Material Balances and conservation laws

With the special Theory of Relativity the law of Conservation of Mass and the Law of Conservation of Energy merge into one law.

So for example in a reaction involving elementary particles the mass + energy(which may now be represented in the same units) of the reactants equals the mass+energy of the products.

See also E=mc².