(The Most Kind)
The All-Pitying, The Compassionate, The Clement.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Ar-Ra’uf (in Arabic: ٱلْرَّؤُفُ), The One who is extremely compassionate. He is The One whose mercy will endow whoever he willed among His creatures. Whatever Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ decrees is done with perfect judgment, and He is never harsh or unjust in his rulings.
From the root ra-hamza-fa (ر أ ف), which has the following classical Arabic connotations: to be kind, gentle, clement, to be merciful, compassionate, to show pity, to show tenderness.
Difference between Raheem and Ra'uf:
The name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ Ar-Rauf, the most kind and compassionate, is mentioned 11 times in the Qur'an. Calling on this name invokes on Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ desire to be tender to His servants. In fact, in the Qur'an, this name is often mentioned in pairs with the names of His mercy. Imam Al-Ghazali writes, "Al-Ra'uf - the All-Pitying - is one who possess pity, and pity is an intensification of mercy."
So in a sense, it's similar to the name Ar-Raheem (The Merciful) but exists as a more intensified or emphatic form. The difference is Allah's Rahma (mercy) is shown after a calamity, whereas Ra'fa is before. Narrated Abdullah: I visited the Prophet ﷺ during his ailments, and he was suffering from a high fever. I said, "You have a high fever. Is it because you will have a double reward for it?" He said, "Yes, for no Muslim is afflicted with any harm but that Allah will remove his sins as the leaves of a tree fall down." 
Here tragedy befalls a person, and he/she has been afflicted with some hardship. But this is not without benefit, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ shows His mercy to that person, and this is atonement from sins. Allah's Messenger ﷺ said: There is no trouble that comes to a believer except that it obliterates from his sins, even if it is the pricking of a thorn. 
These two are examples of Rahma or Allah's mercy. Ra'fa manifests in ways of warnings or protection from things that may cause a person harm. He takes pity and showers His mercy so tragedy can be avoided. To receive Allah's compassion means enjoining good here on earth but also for you in the hereafter. This is a higher form of mercy, by giving His servants warnings of actions that will cause damage. We may not be privy to this kind of compassion which is why Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is always deserving of more than we can offer. In the book, "In the Company of God," it mentions the scholar Abu Ubaydah who said: "Compassion is more delicate a disposition than mercy."
Wallazeena jaaa’oo min ba’dihim yaqooloona Rabbanagh fir lanaa wa li ikhwaani nal lazeena sabqoonaa bil eemaani wa laa taj’al fee quloobinaa ghillalil lazeena aamanoo rabbannaaa innaka Ra’oofur Raheem
"And [there is a share for] those who came after them, saying, 'Our Lord, forgive us and our brothers who preceded us in faith and put not in our hearts [any] resentment toward those who have believed. Our Lord, indeed You are Kind and Merciful.'" — (Qur'an 59:10)
Huwal lazee yunazzilu ‘alaa ‘abdiheee Aayaatim baiyinaatil liyukhrijakum minaz zulumaati ilan noor; wa innal laaha bikum la Ra’oofur Raheem
"It is He who sends down upon His Servant [Muhammad] verses of clear evidence that He may bring you out from darknesses into the light. And indeed, Allah is to you Kind and Merciful." — (Qur'an 57:9)
Wa law laa fadlul laahi ‘alaikum wa rahmatuhoo wa annal laaha Ra’oofur Raheem (section 2)
Dr. Ghali Translation:
"And had it not been for the Grace of Allah upon you and His mercy, and that Allah is Ever Compassionate, Ever-Merciful (you had been the losers)." — (Qur'an 24:20)
Laqat taabal laahu ‘alan nabiyyi wal Muhaajireena wal Ansaaril lazeenat taba’oohu fee saa’atil ‘usrati min ba’di maa kaada yazeeghu quloobu fariqin minhum thumma taaba ‘alaihim; innahoo bihim Ra’oofur Raheem
"Allah has already forgiven the Prophet and the Muhajireen and the Ansar who followed him in the hour of difficulty after the hearts of a party of them had almost inclined [to doubt], and then He forgave them. Indeed, He was to them Kind and Merciful." — (Qur'an 9:117)
Wa minan naasi mai yashree nafsahub tighaaa’a mardaatil laah; wallaahu ra’oofum bil’ibaad
"And of the people is he who sells himself, seeking means to the approval of Allah. And Allah is kind to [His] servants." — (Qur'an 2:207)
The believer benefits from knowing that Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Ar-Ra'uf as it helps to further our relationship with Him. The study of His attributes of mercy and compassion increases our love towards Him as it shows He cares and loves us. We are not left stranded and hopeless. This name communicates a yearning of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ to be empathetic to our struggle and show pity to one who returns to Him. He guides and instructs us in ways that are unseen and saves us from harm, and to Him, we are forever grateful.