Apology dream meaning is explained below using 11 different sources. Each interpretation is shown with its source.

Interpretation 1 — Silvana Amar

This dream always has something to say about our relationships, the relationship that we have with ourselves and/or with others. Apologies are associated with forgiveness and honesty. Thus, consider the details of your dream and consider whether an apology is necessary in order for you to move forward in a particular relationship or with an area of your personal life. Also, another chance could be available to making a relationship workable. Forgive, but do not accept abuse. Be forgiven, but do not dish out abuse. Repattern before you are faced with reliving it over in the same way again. 
Source: The Bedside Dream Dictionary • Author: Silvana Amar

Interpretation 2 — Nancy Wagaman

Regret or remorse.

A desire for peace, harmony, or reconciliation.

Self-righteousness.

Making an apology can represent a guilty feeling, a sense that you owe someone an apology, a real-life apology you’ve made or you’re thinking about.

Someone else apologizing to you can represent: an apology you’ve received in real life or you’d like to receive, your belief that someone owes you an apology, perceiving or imagining that someone is feeling guilty.

See Feeling, Forgiving, Blamed, Being, Blaming, Confronting, Confronted, Being, Denying

Source: The Curious Dreamer’s Dream Dictionary • Author: Nancy Wagaman

Interpretation 3 — Silvana Amar

This dream always has something to say about our relationships, the relationship that we have with ourselves and/or with others. Apologies are associated with forgiveness and honesty. Thus, consider the details of your dream and consider whether an apology is necessary in order for you to move forward in a particular relationship or with an area of your personal life.
Source: The Bedside Dream Dictionary • Author: Silvana Amar

Interpretation 4 — Versatile - Anonymous

Spiritually an apology is an act of self-justification – an understanding of rightness – and it is this meaning that comes across first of all in dreams of such an act.

To dream that we apologize to someone means we acknowledge a lack of integrity in ourselves.

To receive an apology suggests a recognition of that same integrity.

Source: Dream Meanings of Versatile • Author: Versatile - Anonymous

Interpretation 5 — Versatile - Anonymous

Psychological / emotional perspective: It is important that we feel good about ourselves and, as dreams are a way of righting an imbalance, we have a mechanism through apology to put right an act or deed, either our own or others’, which has upset us.
Source: Dream Meanings of Versatile • Author: Versatile - Anonymous

Interpretation 6 — Versatile - Anonymous

Material aspects: If we dream about giving or receiving an apology we are aware of having offended our own personal code in everyday life and can work out what we need to do to restore the status quo.
Source: Dream Meanings of Versatile • Author: Versatile - Anonymous

Interpretation 7 — myjellybean

To dream about an apology, whether you give or receive one, is related to friends. You may lose one friend and gain another, or perhaps you will be surprised by the return of a former friend.
Source: My Dream Interpretation • Author: myjellybean

Interpretation 8 — Stearn Robinson - Tom Corbett

Whether the apology was given or received, this dream in any form pertains to friends.

You may lose (Hie and gain another, or perhaps be surprised by the return of a former one.

Source: The Complete Guide to Interpreting Your Dreams • Author: Stearn Robinson - Tom Corbett

Interpretation 9 — Joan Seaman - Tom Philbin

1. One wants to apologize for something.

2. Another action is necessary to correct something.

Source: New American Dream Dictionary • Author: Joan Seaman - Tom Philbin

Interpretation 10 — Margaret Hamilton

An apology in a dream is true regret revealed to bring about forgiveness and restoration
Source: Dream Dictionary Unlimited • Author: Margaret Hamilton

Interpretation 11 — Internet Archive - Anonymous

A change of companionship; possibly a return to a former friendship.
Source: Mystic Dream Book • Author: Internet Archive - Anonymous