Atomic mass (not to be confused with atomic mass number) refers to the mass of a given atom of a specific isotope, and is often expressed in unified atomic mass units. Atomic mass is found by adding together the individual masses of the protons and neutrons in the nucleus (the mass of electrons is comparatively insignificant). The value displayed on the periodic table is a weighted average based on the relative natural occurrence of all possible isotopes of an element.
What makes atomic mass complicated is the fact that elements come in more than one isotope. Chemists need to know what a given element will actually weigh, in order to know how much to use (and so forth) when working with it in their laboratories, so the atomic mass refers to the actual weight of that element, per atom on the average. This depends upon the isotopes that exist, and also upon the relative abundance of those isotopes. It can only be determined experimentally, it is not something derived from the periodic table. You have to actually weigh the element to find out what it weighs.
*The atomic mass number of an element is the total number of neutrons and protons for a given isotope. For example 14C or carbon-14 has 6 protons and 8 neutrons.