How is a average mass different from a weighted average mass?

Average mass is weighted because there are different naturally-occuring isotopes (types) of each element -- same number of protons, but a different number of neutrons.

For example, there is Carbon-12 (with 6 protons + 6 neutrons) and there is also carbon 13 (6 protons + 7 neutrons) and carbon-14 (6 protons + 8 neutrons).

If C-13 and C-14 present in exactly the same amount as C-12, then the average would be 12 + 13 + 14 = 13. However, Carbon-12 is the most stable and found MUCH more often than the other two isotopes in nature, but C-13 and C-14 are also present in very small quantities. Therefore, the weighted average mass is 12.011...it's not 12.0000 because it reflects C-13 and C-14.