Outside the month of Ramadan, the prophet (S.A.W.S.) advised Muslims to fast three days of each Islamic month.
Some of the ahadith (Prophetic Sayings) on fasting three days of each month are as follows:
It was narrated that Abu Hurayrah (may Allaah be pleased with him) said: My close friend [the Prophet (peace and blessings of Allaah be upon him)] advised me to do three things which I will not give up until I die: fasting three days of each month, praying Duha and going to sleep after Witr. [Narrated by al-Bukhaari (1124); Muslim (721).] (Read the Dua for Witr prayers here)
It was narrated that ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said to me: “It is sufficient for you to fast three days every month, because for every good deed you will have (the reward of) ten like it, so that will be like fasting for a lifetime.” [Narrated by al-Bukhaari (1874); Muslim (1159).]
al-Shaykh Ibn ‘Uthaymeen further elaborated on the ahadith as follows:
It is permissible to fast these days one after the other or separately, and they may be at the beginning of the month, or in the middle, or at the end. The matter is braod in scope, praise be to Allaah, because the Messenger of Allaah (peace and blessings of Allaah be upon him) did not state any specific days. ‘Aa’ishah (may Allaah be pleased with her) was asked: Did the Messenger of Allaah (peace and blessings of Allaah be upon him) fast three days of each month? She said: Yes. It was asked: In which part of the month did he fast? She said: He would not bother in which part of the month he would fast. Narrated by Muslim, (1160). But the 13th, 14th and 15th are better, because these are al-ayyaam al-beed. [Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 10/ question no. 376. ]
Therefore, it should be noted from the ahadith above that although the prophet (s) advised us to fast three days of each month, the 13th, 14th, and 15th were not specified. But the scholars do recommend those days because they are ayyaam al-beed. These days are referred to as Ayaam Al-Beed because the word “Beed” in Arabic is derived from the word “Abyad”, which means white. The three middle days of the 13, 14 and 15 of lunar month are called “Al-Ayyam-ul-Beed” because their nights are bright because of the moonlight.