It is the number of atoms in exactly 12 grams of carbon-12. Make sure you are refering to one gram of carbon 12. If you look at the atomic mass and add all the parts of an element or compound, that weight (if the units are changed to grams) contains 1 mole of atoms or molecules. So, NaCl is (22.99) + (35.45) = 58.44, in grams that would be 6.022x10e23 molecules of salt, technically. A covalent compound would have probably been better as an example.
Since atomic weight on the periodic chart is based off the mass of carbon 12, this is a way to define the molecular weight (absolute mass) of a mole of any pure substance (or 6.022x10e24 individual atoms/molecules).
Anyway, if that doesn't clear anything up, I don't know how to explain it without going into TOO much detail.