Sha’baan is the name of the (eighth) month, and it is so called because in this month the Arabs used to disperse (tasha’aba) in search of water, or it was said that they dispersed to carry out raids and forays. Or it was said that it is so called because it sha’aba (branches out or emerges) i.e., it appears between the months of Rajab and Ramadhaan. 

‘Aa’ishah, may Allaah be pleased with her, said: “The Messenger, sallallaahu alayhi wa sallam, used to fast until we thought he would never break his fast, and not fast until we thought he would never fast. I never saw the Messenger of Allaah, sallallaahu alayhi wa sallam, fasting for an entire month except in Ramadhaan, and I never saw him fast more than he did in Sha’baan.” [Al-Bukhaari and Muslim]

It was reported in the books of the Imaams Al-Bukhaari and Muslim, may Allaah have mercy upon them, that Ibn ‘Abbaas, may Allaah be pleased with him, said:

“The Messenger of Allaah, sallallaahu alayhi wa sallam, did not fast any entire month apart from Ramadhaan.”

Ibn ‘Abbaas, may Allaah be pleased with him, regarded it as disliked to fast any entire month apart from Ramadhaan. 

Ibn Hajar, may Allaah have mercy upon him, said: “He, sallallaahu alayhi wa sallam, observed more voluntary fasts in Sha’baan than in any other month, and he used to fast most of Sha’baan.”

Usaamah Ibn Zayd, may Allaah be pleased with him, said: “I said: ‘O Messenger of Allaah, I do not see you fasting in any other month like you fast in Sha’baan.’ He, sallallaahu alayhi wa sallam, said: ‘That is a month to which people do not pay attention, between Rajab and Ramadhaan, and it is a month in which deeds are lifted up to the Lord of the Worlds. I like for my deeds to be lifted up when I am fasting.’” [An-Nasaa'ee]

Ibn Rajab, may Allaah have mercy upon him, said: “Fasting in Sha’baan is better than fasting in the Sacred Months, and the best of voluntary fasts are those that are (observed in the months) closest to Ramadhaan, before or after.

  The status of these fasts is like that of Al-Sunan Al-Rawaatib (optional prayers which the Prophet, sallallaahu alayhi wa sallam, continued to perform all the time) which are done before and after obligatory prayers and which make up for any shortfall in the number of obligatory prayers. The same applies to fasts observed before and after Ramadhaan. Just as Al-Sunan Al-Rawaatib are better than other kinds of voluntary prayers, so fasts observed (in the months) before and after Ramadhaan are better than fasts at other times.

The phrase “Sha’baan is a month to which people do not pay attention, between Rajab and Ramadaan” indicates that because it comes between two important months, the sacred month of Rajab and the month of Ramadhaan, people are preoccupied with those two months and they do not pay attention to Sha’baan. Many people think that fasting in Rajab is better than fasting in Sha’baan, because Rajab is one of the Sacred Months, but this is not the case.

 Read more here.