The atomic weight of an element (as it appears in the periodic table) is the weighted average of the atomic mass numbers of all of the isotopes for that element.
For example, the atomic weight of carbon (as shown on the periodic table) is 12.011 a.m.u. (atomic mass units). However, there is no one carbon atom that has a mass of 12.011 a.m.u. Carbon exists as four different isotopes: carbon-11, carbon-12, carbon-13, and carbon-14, which have approximate atomic mass numbers of 11, 12, 13, and 14 a.m.u., respectively. If you know the percent abundance of each of those isotopes, you can calculate the atomic weight of carbon by determining the weighted average of the atomic mass numbers of the four isotopes. That weighted average comes to 12.011 a.m.u. The reason that the atomic weight is closer to 12 than it is to the other atomic mass numbers is that carbon-12 is the most common isotope of carbon.
For most elements, the atomic mass number of the most common isotope for that element can be determined by rounding the atomic weight for that element to the nearest whole number. For example, the atomic weight of aluminum is 26.98154 a.m.u. Therefore, the most common isotope for aluminum can be assumed to be aluminum-27.