بسم الله الرحمن الرحيم

‘Āishah asked the Messenger of Allāh sallallāhu 'alayhi wa sallam what should be said in the Night of Qadr, to which he replied, اللَّهُمَّ إِنَّكَ عَفُوٌّ تُحِبُّ الْعَفْوَ فَاعْفُ عَنِّي (O Allāh! Verily, You are One who Pardons, and You love to pardon, so pardon me!)”

O Allāh! Verily, You are One who Pardons (‘Afuww)
Al-‘Afuww is a Name of Allāh. It is often translated to mean the one who pardons or forgives.
 
‘Afuww comes from ‘afw, which means to leave or abandon a thing. It also denotes meanings of growth or abundant increase. 
 
Therefore, Al-‘Afuww means one who leaves or abandons sins and their consequences. In other words, Allāh forgives sins and abandons any form of punishment resulting from that sin. Furthermore, its connection to increase is reflected in the increasing frequency of Allāh exercising this attribute.
 
Essentially, this Name denotes mercifully overlooking a fault and thereafter abandoning the trials and sicknesses resulting from it. 
 
Allāh’s ‘afw with regards to the creation is of two types:

1. General. This is manifested upon the creation in this life. It is not restricted to any set of people. This is why sinners are not taken to account and punished immediately. Instead, He continues to provide for them and give them bounties despite their crimes. Al-‘Afuww continues to withhold or leave off the devastating consequences of their crimes. If it was not for this attribute of Allāh, the entire world would have been engulfed in torment.
    
2. Specific. This is manifested upon the believers only. This is when the believers are forgiven for their crimes and are protected from their consequences in both worlds, but in particular the hereafter. Because of His ‘afw a faction of mankind will not be taken to account at all on the Day of Judgement. This is how Allāh has abandoned their sins. What’s more, there will be another faction that will be taken to account for some of their crimes, but not all. 

You love to pardon (‘afw)
Allāh loves the enactment of this attribute. He loves showing ‘afw and He loves ‘afw being shown.
 
As for Allāh loving this attribute then this hadīth (prophetic narration) alone suffices. He loves it so much that “He pardons (‘afw) a lot” [42:34].
 
As for Allāh loving this attribute being exhibited by others then the following verses clearly prove this point: 
 
“Show forgiveness (‘afw), enjoin what is good, and turn away from the foolish.” [7:199] Allāh does not command something except that He loves it.
 
“Let them pardon (‘afw) and forgive. Do you not love that Allāh should forgive you? And Allāh is Oft-Forgiving, Most Merciful” [24:22]. This verse establishes that forgiveness from Allāh is achieved by forgiving others. Just as we seek to be forgiven, we should forgive others when we are wronged. 
 
So pardon me
The ‘afw that is being sought here is both the general and specific type.
 
Concluding remarks
Know this: Allāh is shy of returning the hands of His slaves empty handed, “Your Lord is Shy and Generous. He is shy to turn away the hands of His slave empty when he raises them to Him” [Ahmad].
 
Know this: Du’ā ought to be said with certainty of answer, “Call on Allāh in a state of certainty about the response. And know that Allāh does not accept a supplication from a heedless heart” [Ahmad].
 
Raise your hands knowing that your Lord is shy and generous, and with certainty and good expectation that He will respond to you before you lower your hands, say, “O Allāh! Verily, You are One who Pardons, and You love to pardon, so pardon me!”

والحمد لله رب العالمين
وصلى الله وسلم على نبينا محمد