He who wills goodness and mercy for all His creatures
Allah is Ar-Rahmaan (in arabic: ٱلْرَّحْمَـانُ). He is the One who blesses all His creation with prosperity and devoid from disparity. He is most merciful, kind, and loving towards all creation. His Rahma is all inclusive and embraces all.
From the root ra-ha-mim (ر ح م), which has the following classical Arabic connotations: to have tenderness, gentleness, kindness to love to have mercy, to have pity to show favor and goodness to have all that is required for beneficence.
We begin the journey to understanding who Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ with the name Ar-Rahman and Ar-Raheem. As a way of developing His relationship with us, He tells us more about Him. The names most frequently used in the Qur'an are the names of Rahmah (i.e., His mercy). We begin every surah with the exception of Surah Taubah with recitation of the Basmala (i.e., the bismillah) in which we proclaim His mercy. The Qur'an is in part a gift from Allah, a sign of His mercy. It also gives the impression that He would like all to know is that He is the most gracious and the most merciful.
There are 57 mentions of the name Ar-Rahman spanning across 16 different chapters of the Qur'an.
Qulid’ul laaha awid’ur Rahmaana ayyam maa tad’oo falahul asmaaa’ul Husnaa; wa laa tajhar bi Salaatika wa laa tukhaafit bihaa wabtaghi baina zaalika sabeela
"Say, “Call upon Allah or call upon the Most Merciful. Whichever [name] you call – to Him belong the best names.” And do not recite [too] loudly in your prayer or [too] quietly but seek between that an [intermediate] way." — (Qur'an 17:110)
In the Qur'an "My mercy encompasses all things" (Qur'an 7:156) and Shaykh Tosun Bayrak writes of this name "He is the one who wills mercy and good for all creation, at all times, without any distinction between the good and the bad, the faithful and the rebel, the beloved and the hated." It is clear from this verse there is no discrimination as to whose worthy of His mercy and compassion.
There are eight names that refer to His mercy and kindness: Ar-Rahman, Ar-Raheem, Ar-Ra'uf, Al-Barr, Al-Wahhab, Al-Ghaffar, Al-Afuww, and At-Tawwab. Each name, although related under the umbrella of mercy, is unique. We'll explore each in detail and see the various ways in which Allah's mercy manifests. As for the name Ar-Rahman it is reserved for Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ alone. It's a quality that can't be ascribed to anybody else. A person can be referred to as Raheem, meaning showing absolute mercy. But Ar-Rahman is understood to be all-encompassing mercy, so far-reaching that it touches everything and everyone. A kind of mercy that knows no bounds. As a name, it is understood this kind of mercy is reserved only for Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. A person named Rahman must therefore have the prefix Abdur, meaning servant of the merciful.
From the hadith, it comments on Allah's Rahmat (mercy), “Verily, Allah has one hundred portions of mercy. From one portion the creation has been given mercy by virtue of which there is mutual love between the people and ninety nine portions are reserved for the Day of Resurrection.” 
Abdullah ibn Amr reported: The Messenger of Allah, peace and blessings be upon him, said, “Those who are merciful will be shown mercy by the Most Merciful. Be merciful to those on the earth and the One in the heavens will have mercy upon you.” 
The belief in Allah's mercy is beneficial to a believer because it causes an individual to reflect on their ability to be merciful themselves. Narrated Jarir bin `Abdullah: Allah's Messenger (ﷺ) said, "Allah will not be merciful to those who are not merciful to mankind."  It also encourages a believer to do good, to act with virtue so that they can receive the mercy of their Lord, "As for those who believe and do good, the Most Compassionate will certainly bless them with genuine love" (Surah Maryam ayah 96)
'Umar b. Khattab reported that there were brought some prisoners to Allah's Messenger (peace be upon him) amongst whom there was also a woman, who was searching (for someone) and when she found a child amongst the prisoners, she took hold of it, pressed it against her chest and provided it suck. Thereupon Allah's Messenger (ﷺ) said: Do you think this woman would ever afford to throw her child in the Fire? We said: By Allah, so far as it lies in her power, she would never throw the child in Fire.' Thereupon Allah's Messenger (ﷺ) said: Allah is more kind to His servants than this woman is to her child. 
Allah's mercy is vast and is described by Prophet ﷺ to be greater than a mother's love for her child. In Imam Zarruq's book, The loftiest goal in elucidating Allah's most beautiful names he recommends attaching oneself to this name through "fellowship, hope, behaving with extreme affection because of firm trust in His affection." Know Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is all-wise and all-knowing, you're forgiveness towards others, and their imperfections will be rewarded on the day of judgment. Lead with hope and compassion and seek to assist those who are misguided as they are in need. And on a concluding note for this name, begin every task by calling upon Ar-Rahman through the phrase, "Bismillah Hir-Rahman Nir-Rahim," which means "In the name of God, The Most Gracious, The Most Merciful." All things are only made possible with Allah's blessing. We, too, require His mercy and grace in all matters.