In relation to its use with reference, it means the person's working ability and probity. A person of good character is one who is reliable and honest. A person of bad character is one who is unreliable and probably dishonest. You do not write your own character reference - it has of necessity to come from someone who has employed you or who has good knowledge of you.
Personality is the personal nature of the individual, the thing that makes him or her different from other people.