The atomic mass of an element is the total number of protons and neutrons in the nucleus of the atom.
Now, here's the rest of the story. The atomic mass of an atom, as given on the periodic table of the elements, is an average. If you had a way to weigh individual atoms one by one, you would find that most of the atoms of a substance had a weight equal to the (rounded) atomic mass, but every now and then you'd have one that was different. The different atoms are called isotopes. They occur naturally, and have an abnormal number of neutrons in the nucleus.
For example, carbon has an atomic mass of 12.0107. In reality, you will never find an atom of carbon that weights 12.0107 amu's. You'll find a lot of carbon atoms that weight exactly 12.000, and a very few that weigh 14.000. For the common size atoms, which we call carbon-12, the weight tells us that there are 6 protons and 6 neutrons in the nucleus. A carbon-14 still has 6 protons (the number of protons is really what determines the identity of the atom), but it has 14-6= 8 neutrons.