They're only truly great who are truly good." 

-George Chapman 

Great is a stronger way of saying good. If you do good, your doing okay. If you do GREAT, the your doing more what is expected of you. For example, in a math test. There are 10 questions. There are 2 extra ones that make a total of 12 questions. The extra 2 are extra credit. One person got 12 out of 10. Their score was good. But you did the extra credit. Your grade was a 12 out of 10.  You got a great score.