1)

JEWISH LAW COURTS TURN AWAY HASH-M'S WRATH

וכתיב (במדבר כה) ויאמר ה' אל משה קח את כל ראשי העם אם העם חטאו ראשי העם מה חטאו אמר רב יהודה אמר רב אמר לו הקב"ה למשה חלק להם בתי דינין מ"ט אילימא משום שאין דנין שנים ביום אחד והאמר רב חסדא לא שנו אלא בשתי מיתות אבל במיתה אחת דנין אלא כדי שישוב חרון אף מישראל
Translation: And it is written (Bamidbar 25:4), "And Hash-m said to Moshe: Take all the heads of the people and hang them before Hash-m, facing the sun, so that the burning wrath of Hash-m may turn away from Israel." If the people sinned, what did the heads of the people do wrong? Rav Yehuda said in the name of Rav: The Holy One, blessed is He, said to Moshe: Appoint for them courts. What is the reason? If you say it is because we do not judge two capital cases in one day-did Rav Chisda not say that this was taught only in a case of two different types of execution, but in one type of execution, they may judge? Rather, it was in order to turn away the wrath of Hash-m from Yisrael.
(a)

How does appointing more Batei Dinim (that can rule on capital cases) turn away the wrath of Hash-m from Yisrael?

1.

Rashi: When Hash-m sees that all are involved in defending His honor, His anger stops.

2.

Iyun Yaakov: Once there are many Batei Dinim in this world, since there is judgment in the lower world, there is no judgment in the upper Heavenly court.

3.

Yad Ramah: When more Batei Dinim are established, evil is eliminated more swiftly, which removes the cause of Divine wrath from the world.

2)

UNDERSTANDING THE PASUK IN YESHAYAHU

דיני ממונות גומרין בו ביום כו': מנהני מילי א"ר חנינא דאמר קרא (ישעיהו א) מלאתי משפט צדק ילין בה ועתה מרצחים ורבא אמר מהכא (ישעיהו א) אשרו חמוץ אשרו דיין שמחמץ את דינו ואידך אשרו חמוץ ולא חומץ ואידך האי מלאתי משפט מאי עביד ליה כדר' אלעזר אמר ר' יצחק דא"ר אלעזר אמר רבי יצחק כל תענית שמלינין בו את הצדקה כאילו שופך דמים שנאמר מלאתי משפט צדק וגו' וה"מ בריפתא ותמרי אבל בזוזי חיטי ושערי לית לן בה
Translation: Monetary cases are completed in the daytime etc. - From where is this derived? From R. Chanina who said - The Pasuk states (Yeshayahu 1:21), "(She - i.e. Yerushalayim - that was) full of justice, in which righteousness would lodge, but now murderers." And Rava said: From here (Yeshayahu 1:17), "strengthen ('Ashru') the robbed ('Chamotz')," which is interpreted as meaning- 'praiseworthy ('Ashru') is the judge who delays ('Mechametz' - 'lets his ruling ferment') his verdict'. The other (i.e. R. Chanina), how does he understand that Pasuk? Strengthen the robbed, but not the robber. And the other (i.e. Rava), how does he understand the Pasuk (Yeshayahu 1:21),"(She - i.e. Yerushalayim - that was) full of justice (in which righteousness would lodge, but now murderers.)"? It as R. Elazar said in the name of R. Yitzchak, as R. Elazar said in the name of R. Yitzchak: Every fast during which the charity delayed overnight (rather than being distributed), it is as if blood is poured out, as it says (Yeshayahu 1:21),"(She - i.e. Yerushalayim - that was) full of justice (in which righteousness would lodge, but now murderers.)" And the teaching applies to (delaying the distribution of) silver and dates, but with money, wheat and barley, there is no problem (to delay it).
(a)

Both our Gemara and the Gemara in Brachos 6b that teaches that 'Agra D'Taanisa Tzidkasah' - 'the main reward for a fast is the charity', show that giving Tzedakah is central to the fast day. Why is it so significant?

1.

Daf Al Daf: The goal of fasting is repentance for rebelling against Hash-m. Chazal teach (Kiddushin 32b) that a king cannot forgo his honor-so how can Hash-m forgive those who dishonor Him? The answer is that Hash-m is not only our King, but also our Father-and a father can choose to forgo his honor. The Gemara in Bava Basra 10a illustrates this through Rabbi Akiva's response to Turnus Rufus: Just as a king, angry at his son, imprisoned him and forbade anyone from feeding him-yet later rewarded the one who showed compassion-so too, Hash-m rewards us for giving to the poor, because we are His children, as it says, "Banim Atem laHashem Elokeichem"-"You are children of Hash-m, your G-d." Through tzedakah, we relate to Hash-m not only as our King, but as our Father - and it is only in that role, where Hash-m can forgo His honor, that our fast can achieve its ultimate goal: true forgiveness.