The person asks from Hashem to give him a heart of pure love and fear of Hashem.
Now, this level of a “pure heart” cannot be attained by any created being by itself, through its own “awakening below,” rather, it is a gift that is given from Hashem Above, at that time of His “shining face,” as explained above.
However, in order to receive this gift from Above, a preparation is required, which is through “fasting” and “making oneself uncomfortable.”
In order to be a proper “vessel” to receive this gift of love and fear of Hashem, a person must refine and humble himself.
Now, already in the times of the Alter Rebbe it was discouraged to afflict oneself physically and to practice excessive fasting, how much more so nowadays. Rather, for the average person nowadays it means to give up on indulgences that a person doesn’t need, such as eating ice-cream on a regular weekday just for the sake of physical enjoyment.
Another person might feel that waking up early to learn Chassidus before Shachris is like “torture,” since he “needs” that extra sleep. When he makes himself uncomfortable by getting up a half hour earlier so he can learn, he is making himself a better vessel to receive the love and fear of Hashem.
Therefore, the custom is that during the Ten Days of Teshuva, “we fast part of the day, but we don’t need to complete the fast.”
In Shulchan Aruch (Orach Chaim, 581:2) it says: “The custom is to fast on Erev Rosh Hashana. Some people who are very scrupulous also fast all of the days between Rosh Hashana and Yom Kippur, (except for Shabbos and Erev Yom Kippur), and so it is proper to do. All of these fasts a person is not obligated to complete (the fast until night when the stars are visible).”
The mandatory fasts, such as the Tenth of Teves, a person is obligated to fast from dawn until night (when stars are visible) unless he is sick and physically unable. However, during these optional fasts of Erev Rosh Hashana and the Ten Days of Teshuva (except for Tzom Gedalya, which is a mandatory fast), a person is not required to fast the entire day until night for it to be considered a “fast.”
It is important to note, that while this custom is mentioned in the Shulchan Aruch, nowadays, most people do not actually perform these “optional fasts” in the literal sense. Rather, they spend more time in prayer and introspection, and try harder to refrain from unnecessary indulgences.
Since, the purpose of these “fasts” is not out of the obligation to fast, but rather that the person be humbled, so that he shouldn’t feel self-satisfied and fill his belly,
The days of mandatory fasting, such as Tisha Be’av, were established to complete the fast the entire day, because of the severity of the day itself and what happened on that day that needs to be corrected. However, these “fasts” are not connected to correcting what happened during those days per se, but rather just to humble the person, so that he should be more serious and introspective. Therefore, he doesn’t need to actually fast the entire day (to fulfill that custom).
Since, a person cannot receive from Above a “pure heart” when he eats to his fill satiation and his belly is full.
