The Oft-Pardoning, The Effacer of Sins, The Eliminator of Sins.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Afuw (in Arabic: ٱلْعَفُوُّ), The One who pardons sins and leaves no trace of any fault. The difference between forgiving and effacing is there will be no trace or record of the offense being committed. It will be as if it had never happened.
From the root ayn-fa-waw (ع ف و), which has the following classical Arabic connotations: to forgive, pardon, to pass over, forgo, absolve, to obliterate all traces, efface, remove, to kill-off, allow to die, to turn away from punishing, not see, annul, to make unapparent, imperceptible, to give spontaneously, to give without constraint, to give more than what is due.
This name compared to other names of forgiveness:
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ loves to forgive His servants. We can see from the previous attributes that much has been said about His forgiveness. He is At-Tawwab (The Ever-Relenting), Ar-Rahman (The Beneficent), Ar-Raheem (The Merciful), Al-Ghaffar (The Forgiver), and Al-Gafoor (The Great Forgiver). Now, we expand to this list by adding another name, Al-Afuw, The Effacer of Sins. He is the one who erases all traces of sin. Forgiveness implies concealment, but the mark of sin still exists on the servant's record. Al-Afuww suggests much more than just forgiving but eliminating it entirely. The view of scholars is the prior names are names of maghfirah (seeking forgiveness) which is different from seeking afw. For example, maghfirah is like forgiving but not forgetting. ‘afw is purification, being reborn, and having a clean slate.
As a name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, Al-Afuw is mentioned for a total of five times in the Qur'an.
in tubdoo khairann aw tukhfoohu aw ta’foo ‘an sooo’in fa innal laaha kaana ‘afuwwan Qadeeraa
ABUL ALA MAUDUDI TRANSLATION:
"(Even though you have the right to speak evil if you are wronged), if you keep doing good -whether openly or secretly -or at least pardon the evil (then that is the attribute of Allah). Allah is All-Pardoning and He has all the power to chastise." — (Qur'an 4:149)
Zaalika wa man ‘aaqaba bimisli maa ‘ooqiba bihee summa bughiya ‘alaihi la yansurannahul laah; innal laaha la ‘Afuwwun Ghafoor
"That [is so]. And whoever responds [to injustice] with the equivalent of that with which he was harmed and then is tyrannized – Allah will surely aid him. Indeed, Allah is Pardoning and Forgiving." — (Qur'an 22:60)
Signs of Allah's mercy:
Once equipped with the knowledge of these attributes, how can someone feel as if they are so reprehensible that they are beyond Allah's mercy when all evidence points to a Lord who shows us He is caring, kind, and loves to forgive? So, we should never feel overwhelmed. We are told in the Qur'an that doubting Allah's mercy is a greater sin than the thing you were worried about in the first place, "O my sons, go and find out about Joseph and his brother and despair not of relief from Allah. Indeed, no one despairs of relief from Allah except the disbelieving people." (Qur'an 12:87) Never give up hope in Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, and never stop trusting in Him for what you're trying to accomplish. Instead, we should focus on what is within our control, and that is seeking His forgiveness and moving toward spreading as much good as we can. The rest is with Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ.
The mercy of Ramadan:
One of the signs of His mercy is giving us the month of Ramadan. A chance for us to return to Him and receive His blessings Narrated Abu Huraira reported Allah's Messenger ﷺ as saying: When there comes the month of Ramadan, the gates of mercy are opened, and the gates of Hell are locked and the devils are chained. 
Narrated Abu Huraira: The Prophet ﷺ said, "Whoever established prayers on the night of Qadr out of sincere faith and hoping for a reward from Allah, then all his previous sins will be forgiven; and whoever fasts in the month of Ramadan out of sincere faith, and hoping for a reward from Allah, then all his previous sins will be forgiven." 
In this month, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ revealed the first verse of the Qur'an establishing the night of decree (laylatul qadr). This is a night said to have more blessings than a thousand months, "Indeed, We sent the Qur’an down during the Night of Decree. And what can make you know what is the Night of Decree? The Night of Decree is better than a thousand months. The angels and the Spirit descend therein by permission of their Lord for every matter. Peace it is until the emergence of dawn." (Qur'an 97:1-5)
Allahumma innaka afuwwun tuhibbul-afwa, fa'fu anni
"O Allah, You are Forgiving and love forgiveness, so forgive me"
When to seek Allah's forgiveness:
It's also worth noting that seeking the forgiveness of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ should not be confined to only when we have knowingly sinned. We know from the sunnah of Prophet Muhammad ﷺ that he engaged in istighfar (seeking forgiveness) over seventy times a day. Narrated by Abu Huraira: I heard Allah's Messenger ﷺ saying." By Allah! I ask for forgiveness from Allah and turn to Him in repentance more than seventy times a day."  In some other narrations this number is reported to be as high as one-hundred times a day.  Now, keep in mind this is a man beloved and protected by Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ who still feared not receiving the grace of His Lord. Abu Huraira reported Allah's Messenger ﷺ as saying: None amongst you can get into Paradise by virtue of his deeds alone. They said: Allah's Messenger, not even you? Thereupon he said: Not even I, but that Allah should wrap me in His Grace and Mercy.
This, however, should not deter us from doing good deeds. In the Qur'an, it mentions how if a person does good, some of his misdeeds will be converted to good, "Except for those who repent, believe and do righteous work. For them Allah will replace their evil deeds with good. And ever is Allah Forgiving and Merciful." (Qur'an 25:70)