The willingness to genuinely apologize is a key ingredient in any relationship, for we are all fallible, all human, all a work in progress. To recognize the pain one has caused in another - even unintentionally - is at the heart of a thoughtful apology.
But what does it mean to offer a full apology and why can this be so hard to do? First, let's consider what doesn't constitute an apology. A real apology isn't just a generic, "I'm sorry", for this doesn't convey a clear understanding of the particular hurt caused in that situation. And a genuine apology is not motivated out of just wanting to have it be over with. "I said I am sorry already, can't we just move on from this." Being tired of talking about it, wanting your partner to be OK with you again, desiring a change in subject or home climate are not good enough reasons. This kind of placating doesn't lend itself to real resolution and it will feel unsatisfying to your partner.
A true apology demonstates an awareness of the pain that your actions have caused. There is a stated understanding as to why it happened or at least a committment to getting to the bottom of it within yourself. Expanding out of this comes reassurance that you will attempt to prevent it from reoccurring. Being able to offer this to your partner not only can help them feel heard, but also communicates to them that you are serious about taking steps to minimize future negative impact on your relationship.
Why are such apologies hard to give? Because it requires that you own your own part of the argument or conflict. It requires a letting go of being "right" or justifying your actions because of how you yourself might have felt 'wronged'. Inherently it is a vulnerable position and as such is uncomfortable. But all this resistance gets in the way of more meaningful relating. By apologizing, you are taking responsibility for your own actions - independent of your partner's - which contributes to the deepening level of trust in your relationship.
Apologies are important whether for 'small' issues or more complicated, hurtful ones. However, they are only as effective as the receiver experiences them. If the apology doesn't come across to your partner as complete and genuine, then be willing to stay with the ongoing dialogue, learn from your partner and in this respect, learn also about yourself.