There once was a chossid who came to the Chiddushei HaRim before Rosh Hashanah. He told his Rebbe: "A whole year went by and I didn’t accomplish much – not in davening, not in learning…I didn’t have a good year." The Chiddushei HaRim told the chossid that with even one second of true teshuva he could fix the entire year, as it states in Gemara: if someone marries a woman on the condition that he is a tzaddik, even if he is a rasha the kiddushin is valid. Why? Because maybe for one second he entertained the thought of doing teshuva and therefore became a tzaddik for that moment.
Rav Aharon Karliner related: On Erev Rosh Hashanah, during mincha, even though the year is practically over, and only a few minutes remain, we still say "Boruch aleinu…es hashanah hazos. Bless this [the past] year." In that one second, the whole year can be rectified.
Yom Kippur
The Mishna in Masechta Shabbos 2:7 states that every Erev Shabbos one should say three things: עשרתם – isartem (Did you give ma’aser from all of the food so we can eat on Shabbos?), ערבתם – iravtem (Did you make sure there is an eruv techumim so we can walk as far as we need?), and הדליקו את הנרות – hidliku es haneros (Are the candles ready for Shabbos?).
Perhaps we should also say this Erev Yom Kippur, Shabbos Shabbason: םתרשע – Did you take advantage of the ten days of teshuva (עשר)? ערבתם – Did you take responsibility and do teshuva for all you did last year (like a guarantor—ערב)? הדליקו – Did you light your neshama (is it on fire to become one with G-d)?
Sukkos
Sukkos is a continuation of the teshuva of Rosh Hashanah and Yom Kippur. On Sukkos, the teshuva is done through simcha. Sukkah – סוכה is roshei teivos "Vayomer Hashem Salachti Chidvarecha."
Sukkos is our time of joy, but we still remember and long for Yerushalayim of old; like the posuk states "Im lo aaleh es Yerushalayim al rosh simchosi." Aaleh – אעלה is roshei teivos of the Arba Minim – esrog, aravos, lulav and haddasim.
Simchas Torah
On Simchas Torah we celebrate what we will learn in the future, not what we’ve learned in the past. As the Kotzker said, "Is there anyone who can say he learned everything already?"