<<admission of guilt>>
This is much more than the glib oft spoken 'I'm sorry' relating to minor issues. An apology is a spoken or written expression of regret for having done something wrong or hurt someone’s feelings. This should be taken one-step further by asking for forgiveness. So although it is hard to admit when we are wrong, it is harder to ask someone to forgive us. Yet owning up to causing another offence or failing to behaviour rightly is humbling. This act of humility is a desirable character quality and builds relationships.
A genuine apology does not include the word 'but' as this is not taking personal responsibility, rather it is making an excuse. Ideally an apology should indicate a commitment to change your behaviour. By dealing with the issue, there will not be the need to repeatedly apologise for unacceptable actions.
A real apology is a request for mercy and forgiveness
others should be a high priority as they impact on each other and affect our whole outlook on life (Mt 5:23,24).
We should genuinely apolgise to others but can't demand it from those who have harmed or offended us. This requires us to extend grace to them, yet when someone comes to us and apologizes for something they did, then we must be gracious and extend forgiveness, "Forgive as the Lord forgave you" (Eph 4:32; Col 3:13).
See also: forgiveness, grace, guilt, mercy, reconciliation, restitution/restore, sorry.