What Does “Rajab is the Month of Allah” Mean?

Rajab is the month of Allah (swt), because it is specifically associated with blessing, mercy and forgiveness. In this month Allah (swt) accepted prayers and supplications of Prophets.

Since Allah (swt) chooses whom He pleases, He made some days and months superior to others and appointed them as “sacred”. ( Zad al-Maad)

“And your Lord creates and chooses whom He pleases...” (Surah al-Qasas, 68)
 
“Lo! the number of the months with Allah is twelve months by Allah's ordinance in the day that he created the heavens and the earth. Four of them are sacred..” (Surah at-Tawbah, 36)

One of the four chosen sacred months mentioned in the ayah above is Rajab which is also of the “three blessed months”. 

Prophet Muhammad (pbuh) states;
 
“Rajab is the month of Allah, Sha’ban is my month and Ramadan is the month of my Ummah (nation)”. (Ajluni,Kashf al-Khafa)
 
Someone then asked him (pbuh):
 
“O Messenger of Allah! What do you mean exactly, when you say that Rajab is Allah's month?”
 
So Prophet (pbuh) explained;
 
“(I call it Allah's month) because it is specifically associated with forgiveness. The shedding of blood is forbidden in this month. Allah (swt) accepted the prayers of Prophets in this month and in it He rescued his saints (awliya) from the hands of their enemies, and because anyone who fasts during this month Allah (swt) forgives him in three ways. The first and second of these are forgiveness for all the sins he has previously committed, and endless virtue for the remainder of his life. As for the third, he will be safe from the thirst on the Day of Judgment.”  (Al-Ghunya li-Talibi Tariq al-Haqq)

One of the prominent scholars of this time Bediuzzaman Said Nursi; 

Badiuzzaman Said Nursi who is one of the prominent scholars of this time states in his commentary that:
 
“.....For if the reward yielded by good works at other times are tenfold, in the month of Rajab they are more than a hundredfold, in Sha‘ban they exceed three hundredfold, and in Ramadan they reach a thousandfold, while on Fridays in Ramadan they reach thousands and on the Night of Power (Laylat al-Qadr) may reach thirty thousand.” (The Rays)