The total number of nucleons- protons and neutrons - in the nucleus of an atom is called the Mass Number.
For example, the most common isotope of fluorine has an atomic number of $$9$$ and a mass number of $$19$$.
The atomic number tells us there are $$9$$ protons in the nucleus (and also $$9$$ electrons in the shells surrounding the nucleus).
The mass number tells us the nucleus contains $$19$$ particles in total. Since $$9$$ of these are protons, the other $$10$$ are neutrons. We call it the mass number because virtually all the mass in an atom comes from the protons and neutrons - electrons weigh about $$1/2000th$$ of the mass of a proton or neutron.