The atomic mass unit, or amu, is 1/12 the mass of one atom of carbon-12. An atomic mass unit has the mass of 1/(6.0221415 * 10^23) grams.
According to HowStuffWorks, an atomic mass unit is defined as the mass of a single proton or neutron. Hydrogen, the lightest element, has an average mass of 1.00794 amu. A carbon-12 atom is made up of six protons and six neutrons, hence 12 atomic mass units. The mass of the electron is considered negligible, therefore electrons are not counted in measuring an atom's atomic mass. One mole of carbon-12 atoms, or 6.0221415 * 10^23 atoms, weighs exactly 12 grams.