All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The Sacred Months are Thul-Qi‘dah, Thul-Hijjaah, Muharram and Rajab. It was narrated on the authority of Abu Bakrah, that the Prophet, sallallaahu ‘alayhi wa sallam, said: "The division of time has returned to its original form which existed when Allaah created the Heavens and earth. The year is of twelve months, out of which four months are sacred: three are successive: Thul-Qi‘dah, Thul-Hijjah and Muharram, and (the fourth is) Rajab, the month of (the tribe of) the Mudhar which comes between Jumaada and Sha‘ baan." [Al-Bukhari and Muslim]
The Prophet, sallallaahu ‘alayhi wa sallam, said it was the month of the Mudhar because the tribe of the tribe of Rabee‘ah would make sacred the month of Ramadan and call it Rajab, while the tribe of the Mudhar made sacred the month of Rajab itself. Hence, the Prophet, sallallaahu ‘alayhi wa sallam, clarified this when he said: "which comes between Jumaada and Sha‘baan." This way he confirmed the soundness of what the tribe of the Mudhar was doing.
As for the multiplication of reward and punishment during these months, some scholars stated this and cited the verse in which Allaah The Almighty Says (what means): {Indeed, the number of months with Allaah is twelve [lunar] months in the Register of Allaah [from] the day He created the heavens and the earth; of these, four are sacred. That is the correct religion, so do not wrong yourselves during them.} [Quran 9:36]
In his commentary on this verse, Ibn Katheer said,
This part: "So do not wrong yourselves during them" means that people should not commit sins during these months as this is more grave than committing them in any other month just as sins are more grave if committed in the Sacred Land. Allaah The Almighty Says (what means): {and [also] whoever intends [a deed] therein of deviation [in religion] or wrongdoing - We will make him taste of a painful punishment.} [Quran 22:25]
Sins are considered of more gravity during the Sacred Months and this is why the blood-money is multiplied during them according to the school of Ash-Shaafi‘i and many other scholars. Blood-money is also multiplied for the one who kills another in the sacred precincts of Makkah or the one who kills someone in the state of Ihraam (ritual consecration).
After that he quoted what was said by Qataadah that oppression during the Sacred Months is graver than oppression at any other time. Oppression at any time is severe, but Allaah The Almighty can make graver whatever He wants.
Al-Qurtubi said,
Do not wrong yourselves during these months by committing sins. This is because when Allaah The Almighty glorifies something from one angle, it becomes inviolable from one aspect, but if He glorifies something from two angles or more, then this matter would then be inviolable from multiple angles and its punishment (for its violation) would be multiplied. This also applies to good deeds as anyone who obeys Allaah during a sacred month and when he is in a sacred land would get more reward than one who obeyed Him in a non-sacred month in a sacred land. Also, whoever obeys Allaah during a non-sacred month in the sacred land would get more reward than one who obeyed Him in a non-sacred month in a non-sacred land. Allaah The Almighty Says (what means): {O wives of the Prophet, whoever of you should commit a clear immorality - for her the punishment would be doubled two fold, and ever is that, for Allaah, easy.} [Quran 33:30]
Allaah Knows best.