The name of Rajab literally means respected, regarded, and admired. There are two important events during the month, namely the birthday of Imam Ali (as) and Prophet Muhammad (pbuh).
Rajab is the time to prepare for Ramadan– spiritually, mentally and physically. The Prophet (PBUH) also said the month of Rajab is the month of absolution, so it's important to seek forgiveness from Allah, in order to gain purification and Divine nearness.