If you dream that you make an apology, it can be a sign that you are feeling guilty in waking life.
Apologizing in a dream can be a message from your unconscious that you have made an error, and you must correct it.
The person that you are apologizing to can be significant. Are you apologizing to an authority figure? That can be a sign that you have violated a rule.
Perhaps you have committed an act that goes against your moral code?
Apologizing to someone who is less powerful than you in a dream can mean that you have taken advantage of your situation and behaved unfairly.
If you dream that you apologize to a stranger, your dream may mean that you have been too harsh with yourself.
A dream that someone apologizes to you can mean that you believe you have been mistreated.