The All-Forgiving, The Forgiving, The One who forgives a lot.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Ghafoor (in Arabic: ٱلْغَفُورُ), He is The One who completely forgives our sins and faults. His forgiveness is unlimited, and He is all compassionate. He is most high; His forgiveness extends to all who turn to him in humility and seek repentance.
From the root ghayn-fa-ra (غ ف ر), which has the following classical Arabic connotations: to cover, veil, conceal, hide to pardon, to forgive, to set aright, to cover a thing, to protect it from dirt.
As we mentioned in the name al-Ghaffar. There are three accompanying names, al-Ghafir, al-Ghaffar, and al-Ghaffur. al-Ghafir connotes His nature of being the forgiver, whereas al-Ghaffar and al-Ghaffur are more grandiose, meaning the great forgiver, the all-forgiving. Linguistically these two names are not synonymous even though both relate to the ideas of His forgiveness and share the same root. Scholars note that al-Ghaffar describes His ability to forgive as being great. It is all-encompassing, doesn't matter the circumstance, the individuals, or the degree of sin. If Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ wills, He can forgive. Al-Ghafur refers to the vastness, perpetual nature of forgiving time after time. Together these three names are mentioned in the Qur'an ninety-eight times. Of these 98 mentions, al-Ghafur appears 91 times.
Nabbi’ ‘ibaadeee annneee anal Ghafoorur Raheem
[O Muhammad], inform My servants that it is I who am the Forgiving, the Merciful. — (Qur'an 15:49)
Nuzulam min Ghafoorir Raheem (section 4)
"As accommodation from a [Lord who is] Forgiving and Merciful." — (Qur'an 41:32)
Innamaa harrama ‘alaikumul maitata waddama wa lahmal khinzeeri wa maaa uhilla bihee lighairil laahi famanid turra ghaira baaghinw wa laa ‘aadin falaaa isma ‘alaih; innal laaha Ghafoorur Raheem
"He has only forbidden to you dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah. But whoever is forced [by necessity], neither desiring [it] nor transgressing [its limit], there is no sin upon him. Indeed, Allah is Forgiving and Merciful." — (Qur'an 2:173)
From this name, we learn the importance of maghfira, which means to seek the forgiveness of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. The believer benefits in knowing that Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is al-Ghaffur because it reminds us that we worship an oft-forgiving Lord. Despite making the same mistake repeatedly, we're not doomed by our past.
Narrated Abu Huraira: I heard the Prophet ﷺ saying, "If somebody commits a sin and then says, 'O my Lord! I have sinned, please forgive me!' And his Lord says, 'My servant has known that he has a Lord who forgives sins and punishes for it, I therefore have forgiven my servant (his sins).' Then he remains without committing any sin for a while and then again commits another sin and says, 'O my Lord, I have committed another sin, please forgive me,' and Allah says, 'My servant has known that he has a Lord who forgives sins and punishes for it, I therefore have forgiven my slave (his sin). Then he remains without Committing any another sin for a while and then commits another sin (for the third time) and says, 'O my Lord, I have committed another sin, please forgive me,' and Allah says, 'My servant knows that he has a Lord who forgives sins and punishes for it. I have forgiven My servant - three times.'" 
A du'a from Abu Bakr al-Sadiq (ra), "O Allah, You know me better than I know myself, and I know myself better than these people who praise me. Make me better than what they think of me, and forgive those sins of mine of which they have no knowledge, and do not hold me responsible for what they say."  This covers an essential aspect of the names that share the root gh-f-r. It's not just a name of forgiveness but the idea of concealment. But not in a conniving way, to conceal something ugly and to beautify it. Allah conceals our faults from being exposed, so we're not under public scrutiny. It should inspire us to become better knowing we've been given a second, third, or fourth chance and to help uplift others. So, His mercy extends to forgive perpetually and to hide our faults from being exposed.
Abu Huraira reported Allah's Apostle ﷺ as saying: The servant (whose fault) Allah conceals in this world, Allah would also conceal (his faults) on the Day of Resurrection.  and in a different narration, Abu Huraira reported Allah's Apostle (ﷺ) as saying: The servant (who conceals) the faults of others in this world, Allah would conceal his faults on the Day of Resurrection. 
The analogy often used is that every time we sin, a crack appears, which uncovers or exposes us. When we ask for istighfar (seeking Allah's forgiveness) - we're asking for Him to show us His mercy, to protect us by repairing or covering what's been exposed. Indeed Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is both al-Ghaffar (the great forgiver), the one who forgives big and small sins, and al-Ghaffur (the oft-forgiver), the one who forgives time and time again. The only exception is, "Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. And he who associates others with Allah has certainly fabricated a tremendous sin." (Qur'an 4:48) His forgiveness covers all except shirk. But if He wanted to forgive shirk, it's not that He's unable to. Allah knows best.