Rambam (Hilchos Teshuvah 1:1) writes, "If a person committed an aveirah, he must say viduy before Hashem, as it states עשו אשר חטאתם את והתודו, 'They should confess their sins.' This is a mitzvas asei."
The Maharal (Nesivos Olam) compares saying viduy to a man kneeling before his fellow man to beg forgiveness. The man he is speaking to bends down to hear what he is saying, and their faces are very close. This represents the very close connection between Hashem and the Yid when he says viduy and begs for forgiveness.
Bilaam also said viduy. When he saw the malach standing before him, he said חטאתי, "I have sinned," and the Midrash writes, "Bilaam was a clever rasha. He knew that his only protection from punishment was teshuvah. And indeed, when he said חטאתי, he was spared." The Beis Yisrael zt'l said it's a mitzvah to publicize this Midrash, particularly to bachurim (who often feel that Hashem won't forgive them). Even the rasha Bilaam attained forgiveness through viduy (even though his teshuvah was insincere).
Once, after the viduy of Yom Kippur, the chazan of Zaslav said, "Ribono Shel Olam, if the Jewish nation hadn't sinned, where would you hear such a sweet Ashamnu?" Rebbe Zusha of Anipoli zt'l would say, "If the Jewish nation hadn't sinned, where would Hakadosh Baruch Hu get a ונסלח such as the Jewish nation says on Yom Kippur night, with such a tune and outpouring of the soul?"
When you say viduy and ask for forgiveness, Hashem forgives you right away. The Baal HaTanya (Igeres HaTeshuvah 11) proves this from the brachah לנו סלח in Shemonah Esrei. Immediately after we request Hashem to forgive us, we thank Hashem for doing so, as we say, לסלוח המרבה חנון 'ה אתה ברוך. But behold, when one is in doubt about a brachah, he mustn't recite it, lest his brachah be in vain. How can we bless Hashem for forgiving us? Perhaps Hashem didn't accept our teshuvah and didn't forgive us? The answer is: We have no doubt. After one says לנו מחל לנו סלח, he is forgiven. And if we won’t sin again, we will immediately be redeemed, as the following brachah states, גואל 'ה אתה ברוך ישראל ."
The Noam Elimelech zy'a writes, "The Torah teaches us to say viduy with confidence in Hashem's compassion and belief that Hashem forgives our sins. One shouldn't say viduy with sadness and yeush, as that attracts dinim; rather, say viduy with bitachon. Trust that He will forgive you. As it states (Mishlei 28:13), ירוחם ועוזב ומודה, 'he who confesses and abandons [his sins] will obtain mercy.'"
The Viduy is organized in alphabetical order: זלנו'ג גדנו'ב שמנו'א and so on. The Reishis Chachmah explains that our aveiros tainted all the letters of the alef beis, which are the letters of Creation, and we correct them with the viduy. However, notes the Reishis Chachmah, the first word of the viduy is חטאנו, as we say ...חטאנו ואבותינו אנחנו אבל. Why don't we begin with אשמנו? The Reishis Chachmah answers that we begin viduy with חטאנו because this word removes the mekatreg (the Satan). If we were to start by saying our aveiros, the Satan could go up to heaven and say, "Listen to what he's saying. He agrees that he has sinned." But after we said חטאנו, the Satan is silenced. He can't speak out against us. And now we can say the detailed viduy in the order of the alef beis.
In the era of the Beis HaMikdash, there was a mitzvah called viduy maasros, to go to the Beis HaMikdash twice in seven years to proclaim that we observed all the halachos of maasar, terumah, and the like. Surprisingly, this mitzvah is called viduy. We know that viduy is about confessing one's sins; why is it now used to proclaim that "I kept the halachos"? For example, by viduy maasros, one says, שכחתי ולא ממצותיך עברתי לא, "I didn't transgress your mitzvos, and I didn't forget" (Devarim 26:13). Why are these words called viduy (confessions)?
Rebbe Shalom Chaim of Koidenov zt'l answers that both Hashem and the person are speaking in these pasukim: The person says, ממצותיך עברתי, "I transgressed your mitzvos," and Hashem replies, עברתי לא "you didn't transgress." The person says, שכחתי, "I forgot to keep the mitzvos," and Hashem responds, שכחתי לא, "You didn't forget." This is because the viduy wipes away sins entirely.
