The month of Shaban is one of the twelve months in Islam. The Islamic or Hijri calendar is a lunar calendar. It contains 12 months that are based on the motion of the moon. Islamic calendar is consistently shorter than a solar year by about 10 days every year, and therefore it shifts with respect to the Gregorian calendar. 
There are twelve months in Islamic Calendar as mentioned in Qur’an: “Verily, the number of months with Allaah is twelve months (in a year), so was it ordained by Allaah on the Day when He created the heavens and the earth; of them four are Sacred (i.e. the 1st, the 7th, the 11th and the 12th months of the Islamic calendar). That is the right religion, so wrong not yourselves therein” Quran Surah Tawbah 9:36
It was narrated that 'Aishah(R) said: "The Messenger of Allah used to fast (all of) Shaban except a little." Sahih Al Bukhari 1970 and Muslim 1156 andSunan an-Nasa'i Vol3: 2355
Usamah bin Zaid(R) said: "I said: 'O Messenger of Allah, I do not see you fasting any month as much as Shaban.' He said: 'That is a month to which people do not pay much attention, between Rajab and Ramadan. It is a month in which the deeds are taken up to the Lord of the worlds, and I like that my deeds be taken up when I am fasting."' Sunan an-Nasa'i Vol.3:2357
Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “When Sha’baan is half over, do not fast.” Classed as saheeh by al-Albaani inSaheeh al-Tirmidhi, 590, Abu Dawood 3237, al-Tirmidhi 738 and Ibn Maajah 1651
Al-Nawawi said: In the words, “He used to fast all of Sha’baan, he used to fast Sha’baan except a few days” the second phrase explains the first, and indicates that the word “all” means “most of”.
This hadeeth indicates that it is permissible to fast after halfway through Sha’baan, but only for those who are continuing after fasting before halfway through the month.