In Judaism, confession (Hebrew וִדּוּי Widduy; Viddui) is a step in the process of atonement during which a Jew admits to committing a sin before God. In sins between a Jew and God, the confession must be done without others present (The Talmud calls confession in front of another a show of disrespect). On the other hand, confession pertaining to sins done to another person are permitted to be done publicly, and in fact Maimonides calls such confession "immensely praiseworthy".
The confession of a sin in itself does not bring immediate forgiveness, but rather it marks a point in time after which a person's demonstration of the recognition and avoidance of similar future transgressions show whether he or she has truly recovered from the sin and therefore whether he or she deserves forgiveness for it.
Vidui is not found as a noun in the Hebrew Bible, but the concept of confession, and the hithpael verb form of yadah (ידה) from which vidui is derived, are found, such as "Then they shall confess (הִתְוַדּוּ) their sin which they have done" Numbers 5;7, and seems to fall into the category of speech actions.
On Yom Kippur the High Priest confessed his sins and those of Israel onto a goat. Moses is instructed by God in Leviticus 16:21 to speak to Aaron:
He is to "וְהִתְוַדָּה עָלָיו", "confess upon it". In modernity this is part of the Torah Reading for Yom Kippur morning and referenced in the recitation of the Avodah Service during Musaf.
Maimonides, in his book Mishneh Torah writes in Hebrew:
Translation:
How does one confess? [He or she] says: 'Please God! I have intentionally sinned, I have sinned out of lust and emotion, and I have sinned unintentionally. I have done [such-and-such] and I regret it, and I am ashamed of my deeds, and I shall never return to such a deed.' That is the essence of confession, and all who are frequent in confessing and take great value in this matter, indeed is praiseworthy.
In addition to each person's own personal confessions, a form of confession has been added to the daily prayer. There are two accepted structures of confession, the abbreviated confession (וידוי הקטן) and the elongated confession (וידוי הגדול), with both including a list of sins that a person confesses to in the order of the Alephbet; the abbreviated confession lists one sin per letter and the elongated lists two.