The Rambam famously wrote in Hilchos Teshuvah 3:4 that “Although the blowing of the shofar on Rosh Hashanah is a decree from Hashem, there is a remez (reason) behind its blowing. The reason is that the sound of the shofar is to remind us to wake up from our slumber and inspect our actions, do teshuvah, and remember our Creator. And those who have forgotten the truth and wasted their time should look into their souls and inspect their way of life. They should leave the wrong path that they find themselves on.”
Evidently, the Rambam believes that on Rosh Hashanah one should do teshuvah, as he says that the shofar is intended to awaken us to do teshuvah. Similarly it would seem that one should do teshuvah on Rosh Hashanah, as it is part of the Aseres Yemei Teshuvah (10 Days of Repentance).
The Rambam says in the second perek of Hilchos Teshuvah that the mitzvah of teshuvah is comprised of four components: vidui (confession), charatah (regret), azivah (stopping oneself from sinning again), and kabbalah (resolution). The Rambam also says that one must verbalize his confessions in order for it to be valid (vidui b’peh).
The Achronim are bothered by the following question: Why don’t we find the teshuvah process to be a part of the Rosh Hashanah davening – as we do on Yom Kippur? Similarly there are no minhagim to do teshuvah on Rosh Hashanah. Some even have the custom to not eat foods that have the same gematria as the word “chet” (sin). So if the shofar blasts remind us to do teshuvah, why don’t we do any of the teshuvah process on Rosh Hashanah?
The Gemara in Kiddushin 49b says that if one says to a woman “be mekudeshes (betrothed) to me on the condition that I am a tzaddik gamur (complete tzaddik)” and she accepts, the kiddushin is valid even if he is known to be a rasha gamur (complete sinner). This is because perhaps he was meharher b’teshuvah b’libo (thinking of teshuvah in his heart). The Minchas Chinuch (Mitzvah 364) is bothered by how the kiddushin can be valid when it was contingent on the fact that the man was a tzaddik gamur, while he was known to be a rasha gamur? In order for him to become a tzaddik gamur he would have to go through the lengthy process of teshuvah that, at the very least, entails a verbal confession. How could he have accomplished all of that so quickly, and how did the witnesses not hear him repent?
The Sefer Harirai Kedem and Rav Moshe Shmuel Shapiro, zt”l, explain that the teshuvah of Rosh Hashanah is different from that of Yom Kippur, and that of the mitzvah of teshuvah in general. The mitzvah of teshuvah indeed requires the abovementioned four-step process, and that is what we do on Yom Kippur as well. This form of teshuvah atones for and wipes clean one’s sins. However, on Rosh Hashanah we do not do teshuvah on individual sins; rather, as the Rambam said regarding the shofar blasts, this teshuvah is to awaken us from our sleep, remember our Creator, look into our souls, stop wasting our time with nothingness, and leave the wrong path and return to the right path. With the teshuvah of Rosh Hashanah, one does not remove any of his individual sins; instead he changes his direction, and outlook on life. Rosh Hashanah, the beginning of the 10 Days of Repentance, is the first step in the teshuvah process. The days following Rosh Hashanah are focused on the mitzvah of teshuvah for individual sins – with Yom Kippur at the climax.