Yom Kippur Katan (יום כיפור קטן translation from Hebrew: "Minor Day of Atonement"), is a practice observed by some Jews on the day preceding each Rosh Chodesh or New-Moon Day, the observance consisting of fasting and supplication, but being much less rigorous than that of Yom Kippur proper.
The custom is of comparatively recent origin and is not mentioned in the Shulchan Aruch. It appears to have been inaugurated in the sixteenth century at Safed by the kabbalist Moses Cordovero (Da Silva, "Peri Ḥadash," Rosh Ḥodesh, § 417), who called the fast Yom Kippur Ḳaṭan; and it was included by Isaac Luria in his Seder ha-Tefillah. R. Isaiah Horowitz refers to it by that name, and says it should be observed by fasting and repentance: "Following the custom of the very pious, one must repent of his ways and make restitutions both in money and in personal acts, in order that he may enter the new month as pure as a new-born infant" (Shelah, ed. Amsterdam, 1698, pp. 120b, 140a, 179a). When Rosh Ḥodesh occurs on a Sabbath or Sunday, Yom Kippur Ḳaṭan is observed on the preceding Thursday. The fasting is not obligatory, and only the very pious observe that act of self-denial.
The custom has roots in scripture (Numbers 28;15) where a Korban Hatat (Sin Offering) is ordered for Rosh Hodesh, indicating judgement and atonement is provided by God on that day. Therefore the idea of fasting would seem obvious. However, fasting is prohibited on Rosh Hodesh and thus the sages instituted the fasting on the day prior to Rosh Hodesh.
The liturgy of the day, which consists of selichot, is recited at the Mincha prayer in the afternoon. Tallit and tefillin are adjusted, and if there are among the congregation ten persons who have fasted, they read from the scroll Va-Yechal (Ex. 32:11 et seq.). The selichot are taken partly from the collection used on the general fast-days and Yom Kippur, with the Viddui ha-Gadol (the great confession of sin by Rabbenu Nissim) and Ashamnu, and also a beautiful poem written for the occasion by Leon of Modena and beginning with Yom zeh. Some congregations add Avinu Malkenu. The fast ends with the Mincha prayer. For the text see Baer, 'Abodat Yisrael, pp. 317–319; Emden's Siddur Bet Ya'aḳob, ed. Warsaw, pp. 212a-216b.
Yom Kippur Katan is not observed on the day before Rosh Hashanah. It is not observed prior to Rosh Chodesh Cheshvan, because Yom Kippur has just passed. It is not observed before Rosh Chodesh Tevet, because that day is Hanukkah. It is not observed prior to Rosh Chodesh Iyar, because one may not fast during Nisan.