Rajab, being the seventh month of the Islamic calendar is a stepping stone to the auspicious months of Sha'baan and Ramadaan. Rajab is from the Ashur Hurum (Sacred months), one of four such months in which battles were prohibited. When the moon of Rajab was sighted, Rasullulah (SAW) would recite the following Dua:
Allahumma baarik lana fee rajaba wa sha'bana wa ballighna ramadaan.
"Oh Allah, grant us blessings in the months of Rajab and Sha'baan and make us reach the month of Ramadaan"
(Shu'abul-Imaan and Ibnus Sunni)
This Dua should be recited regularly in the months of Rajab and Sha'baan. In preparation for Ramadaan, the relevance of Rajab may be understood as the month to sow seeds (good actions), Sha'baan is the month in which we should water those seeds (with tears of remorse) and Ramadaan is the month in which we reap the harvest.
Whilst the arrival of Ramadaan is certain, no person is guaranteed reaching Ramadaan. Rasullulah (SAW) would express his eagerness to be blessed with the month of Ramadaan from Rajab. We should therefore become more inclined towards virtuous deeds and Ibadah in these months.
May Allah Ta'ala let us all reach Ramadaan and grant us the ability to spend it in a manner most pleasing to Him. Ameen.