These days are called three white days because the full moon shines at their nights.
Scholars explained how doing fast of these days as fasting the whole life by saying that
The good deed (hassanat) is rewarded 10 times its value
So if any one fasts those 3 days then it will be as fasting (3*10 = 30 days = 1 month), and if he keep doing that every month it will be as fasting the whole life.
The 3 white days are the 13, 14, and 15 of each hijri islamic (lunar) month.
Inshā' Allāh for Sha'bān 1427, these days fall on:
13th – Wednesday 6th September
14th – Thursday 7th September
15th – Friday 8th September
Abu Hurayrah (may Allaah be pleased with him) said: “My close friend [i.e., the Prophet (peace and blessings of Allaah be upon him)] advised me to do three things which I will never give up until I die: fasting three days each month, praying Duha, and sleeping after praying Witr.” (al-Bukhaari, 1178; Muslim, 721).
It is mustahabb to observe this fast in the middle of the hijri month, on the days called Ayaam al-Beed.
It was narrated that Abu Dharr said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) said to me, ‘If you fast any part of the month then fast on the thirteenth, fourteenth and fifteenth.’” (al-Nasaa’i, 2424; Ibn Maajah, 1707; Ahmad, 210)
Fasting will be an intercession for the slave on the Day of Resurrection, when it will say: “O Lord, I stopped him from eating and drinking during the day, so let me intercede for him.” (Reported by Ahmad, 2/174; al-Bayhaqi classed its isnaad as hasan in al-Mujtama’, 3/181; see also Saheeh al-Targheeb, 1/411).
“The smell (coming from the mouth of) the fasting person is better in the sight of Allaah than the scent of musk.” (Muslim, 2/808).
Fasting is something which is just for Allaah, and Allaah will give multiple rewards without measure for it. The hadeeth says: “[Allaah says:] Fasting is Mine and it is I Who give reward for it.” (Al-Bukhaari, Fath, no. 1904)
“Fasting is a protection and a strong fortress against the Fire.” (Reported by Ahmad, 2/402; see also Saheeh al-Targheeb, 1/411 and Saheeh al-Jaami’, 3880)
“Whoever fasts one day for the sake of Allaah, Allaah will keep his face seventy years’ distance away from the Fire because of it.” (Reported by Muslim, 2/808)
“Whoever fasts a day seeking the pleasure of Allaah and then dies [i.e. that is the last thing he does] will enter Paradise.” (Reported by Ahmad, 5/391; see also Saheeh al-Targheeb, 1/412)
“The prayer (du’aa’) of the fasting person will not be refused.” (Reported by al-Bayhaqi, 3/345; see also al-Silsilah al-Saheehah, 1797)[/B]
The Prophet Muhammad (peace be upon him) said:
“Honor scholars, as they are the inheritors of the prophets. Anyone who honors them has honored God and His Messenger.”