From the fullness of his grace we have all received one blessing after another. For the law was given through Moses; grace and truth came through Jesus Christ.
The Law of Moses was not the fulness of grace. The fullness of grace came with the Messiah. There are many interpretations of the word grace. I guess «undeserved kindness» is one of the best. The Law explains to us what God considers to be sin, and the punishment we deserve. Grace takes away the punishment, pays for our transgressions and set us free. The full truth of the Law became known to men, when it was explained by Jesus the Son of man.