What is the reason for naming the 14th, 15th, and 16th days of each month as "Ayyam al-Bid" (the White Days), and what is the ruling on fasting them?

The White Days (Ayyam al-Bid) were named as such because their nights become white (illuminated) by the moon, which appears in them from beginning to end. The correct expression is to say "Ayyam al-Bid" (Days of the White) by adding "al-Bid" as an adjective, because "al-Bid" describes the nights. These days are the thirteenth, fourteenth, and fifteenth of the lunar month.