Ideas behind Fast Days
The Mishna says that on fast days an elderly, learned man would announce:
My brothers! Regarding the people of Ninveh, it does not say "And
G-dsaw their sackcloth and their fasts." Rather it says "And G-dsaw their deeds, that they returned from their bad ways" (Yonah 3:10), and in the Nevi’im it says "Rip your hearts and not your clothing [and return to G-d]"(Yoel 2:13; see Ta’anit 15a).
The point of this was to make it clear to the people that
G-dis not primarily concerned with their external fasts, but instead with the teshuva (repentence) that accompanies them (see Meiri). In this light, the fast is only meant to be an intermediary that helps one achieve teshuva.
Similarly, the Rambam writes regarding those fast days that were instituted to commemorate days when tragedies occurred:
We fast on days of calamities because it arouses our hearts and opens paths to repentance for us. It serves as a reminder of our wicked ways, and that of our ancestors which resemble our present ways, and which thereby brought these calamities upon them and upon us; so that through remembering these things we will return and [fix our ways], as it says, "They will confess their sins and their fathers' sins." (Hilchot Ta’anit 5:1)
Day of Reflection
Since fasting is only a preparation for teshuva, the commentaries point out that those who spend the day fasting while involving themselves with idle activities have grabbed onto the secondary point of fasting and missed the main and essential part. Fast days are meant to be days of reflection and teshuva — and not days when one tries to busy himself with activities to distract himself from fasting (see Mishna Berurah 549:1 in the name of the Chayei Adam).
On fast days one should try and fulfill the three prerequisites of teshuva, namely: 1. Verbally confessing one's sins, 2. Regretting ones sins, and 3. Accepting upon oneself not to repeat them, by coming up with a plan to prevent going back to his old ways. As an aid to accomplish this, the Pele Yoetz says that it is a good idea to occupy oneself with books that bring one to teshuva on this day. Based on this idea, Rav Sternbuch says that is important to remember that even those who are exempt from fasting for medical and other reasons are still obligated in the purpose of the fast, which is to do teshuva (Teshuvot V'Hanhagot vol. 3, 154).
Teshuva through Fasting
We mentioned above that the point of fasting is to help one do teshuva. How does fasting contribute to teshuva? There are many verses that point out how satiation leads to overconfidence and independence, which in turn makes it more likely for a person to transgress. As the Torah says: "The people sat to eat and drink, and they got up to revel" (Shemot 32:6), and "Yeshurun (another name for the Jewish People) got fat and kicked (sinned)" (Devarim 32:15). By fasting, a person feels how low he is — that not eating for merely a day weakens him, and thus causes him to humble himself. This character trait of being humble, in turn, helps him stay away from sinning (Reishit Chochma, Shaar HaTeshuvah, perek 4; Tziporen Shamir of the Chida; Pele Yoetz).
Another way that fasting contributes to teshuva is by its resemblance to sacrificing a korban. Many sins require bringing a korban for complete teshuva. The Gemara says that just like the fats of the korbanot were consumed in the fire after they were slaughtered, so too when a person fasts his body burns fat to make up for the lack of nutrients he is ingesting.
G-dconsiders this as if the person brought a korban (Berachot 17a). Based on this idea some have the custom to learn about korbanot on fast days, as it says in Hoeshea 14:3, "Let our lips (our recitation of the verses having to do with korbanot) take the place of the bull [offerings]." Here, too, the commentaries point out the importance of teshuva, because otherwise, it says in Mishlei 21:27: "The offering of the wicked is an abomination" (see Tziporen Shamir of the Chida and Pele Yoetz "Taanit").
Another way that fasting contributes to teshuva is understood based on the Gemara that in order to receive full atonement for some sins, in addition to teshuva one is also required to go through some suffering (Yoma 86a). The distress that one feels on a fast day can help fulfill this requirement and thereby lead to receiving full atonement (see Reishit Chochma, Shaar HaTeshuva, perek 4).
The commentaries point out that one must be especially cautious from becoming angry on these days since one is easily angered when he is hungry. The severity of getting angry, which Chazal say is in a way comparable to the sin of worshipping idols, can then outweigh the benefits of fasting (Sefer Hayashar, Sefer Chasidim 617, Reishit Chochma Shaar Hateshuva 4, Pele Yoetz "Taanit").
The Gemara says: Mar Zutra says the [main] reward of a fast is the tzedaka that one gives on that day (Berachot 6b). The Maharsha explains this to mean that one should give away the money he saved from refraining from eating and drinking, so that he will not have personal gain even from the money he saved from not eating on that day. According to this, one should give to tzedaka at least the price of his daily meals. The Ketav Sofer adds that a person who fasts begins to personally experience hunger and therefore gives tzedaka to help the poor, who don’t have enough money for food, from also going through this feeling. It is worth adding that, in general, giving tzedaka also helps one receive atonement on a fast day, since where the theme is teshuva and atonement it is proper to give tzedaka.
May we all merit making the most of fast days, and thereby merit seeing the day when they will turn to days of rejoicing with the coming of Mashiach speedily in our days.