The Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204), in the second chapter of his Hilchot Teshuva (Halacha 6), describes the unique opportunity presented to the Jewish people during the ten days from Rosh Hashanah through Yom Kippur. He writes (listen to audio for precise citation) that although Teshuva is always beneficial, on any day throughout the year, this ten-day period is especially propitious for earning atonement for one's misdeeds. The prophet Yeshayahu (55:6) declares, "Seek out Hashem when He is available," and tradition teaches that he speaks here of the period from Rosh Hashanah through Yom Kippur, when God makes Himself "available" and is especially receptive to our prayers and repentance.
The Rambam then qualifies this concept, noting that it applies only to individual prayer and repentance. When a community assembles to beseech God, however, their prayers are accepted at any time throughout the year, and not merely during the Ten Days of Repentance.
In the next passage (Halacha 7), the Rambam speaks of the unique status of Yom Kippur as the day especially designated for repentance and atonement. All Jews must verbally confess and repent on this day. Accordingly, in each of the five prayer services on Yom Kippur (Arvit, Shaharit, Musaf, Minha and Ne'ila) we add the "Viduy" (confessional) in which we solemnly confess our sins before God and beseech Him for forgiveness. The Rambam adds that during the private Amida prayer, the "Viduy" is appended at the end of the prayer, whereas in the Hazzan's repetition of the Amida, "Viduy" is recited as part of the fourth Beracha of the Amida prayer.
Finally, the Rambam writes that one must recite "Viduy" already on Erev Yom Kippur, before eating the Se'uda Ha'mafseket (final meal before the fast). The reason, he explains, is that one might choke on his food and die before reciting the "Viduy," in which case he will have missed the opportunity to confess his sins and repent on the special day on Yom Kippur. We therefore recite the "Viduy" during the Minha service on Erev Yom Kippur, before proceeding to eat the "Se'uda Ha'mafseket."
Summary: Although repentance is valuable and beneficial at all times, the period from Rosh Hashanah through Yom Kippur is a particularly propitious time for repenting. All Jews must verbally confess their sins and repent on Yom Kippur, and thus the "Viduy" (confessional) is recited in each prayer service throughout Yom Kippur, beginning with Minha on Erev Yom Kippur, which one should recite prior to the final meal before the fast.
