Out of His great love for His people, G‑d seeks to be merciful, and would prefer that man repent rather than perish, so that He might grant him good in the end.
He therefore awaits and anticipates the repentance of those who transgress. In His abundant mercy, He granted us special days when He is closest to us, so that our penitence might be immediately accepted.
As the verse (Isaiah 55:6) states: Seek G‑d when He is to be found, call out to Him when He is near.
Our sages commented: This teaches us that there are times when G‑d is to be found and times when G‑d is not to be found, times when He is near and times when He is not near. When is He to be found and near? In the ten days between Rosh Hashanah and Yom Kippur.
Therefore, even though repentance and prayer are always appropriate, they are especially appropriate in the ten days between Rosh Hashanah and Yom Kippur, and are immediately accepted.
During these days, additional prayers are recited, and we are especially careful in fulfilling mitzvot. In some communities, special selichot [penitential prayers] are said before dawn.
It is fitting for a person to decrease his involvement with worldly occupations during these days, and to increase his study of Torah and practice of charity.
The pious and G‑d-fearing take care of their debts and obligations before Yom Kippur.
Scrupulous people who are eager to perform mitzvot make a point of buying an especially beautiful etrog early, during these ten days.
During the entire period of the Ten Days of Repentance, some have the custom of adding a word to the kaddish prayer: the word l’eila [“beyond”] is repeated, and we say “L’eila ul’eila.” Others, for example the Chabad community, add the word only during the Neilah prayer on Yom Kippur.
The year-round wording alludes to the exaltation of G‑d beyond all earthly benediction; the doubled usage for the Ten Days of Repentance bespeaks an even greater divine exaltation, in keeping with the central motif of the Days of Awe—the acceptance of divine sovereignty. In addition, since the specified total number of words in the kaddish has a particular significance, we contract two other words, so that the total number of words remains constant [instead of min kol birchata, we say mi-kol birchata].