Essentially, average mass is unweighted (each entry has equal weight) while for weighted average mass, each entry has a weighting factor multiplied into it. An example will suffice. Chlorine has two stable isotopes, Cl35 and Cl37. The average mass of these would be 36. However, 75 percent of natural chlorine is Cl35 and 25 percent is Cl37. So the averaged mass is
0.75 x 35 + 0.25 x 37 = 35.5.
If you check the Periodic Table, this is the value you see for chlorine.