"A Day of Divine Goodwill"
A fast day is described as "a day of Divine goodwill." 
One reflection of G-d's favor is the Torah reading of the Thirteen Attributes of Mercy in the morning and afternoon services, for these attributes are a manifestation of unbounded Divine benevolence.
Similarly, the positive nature of a fast day is demonstrated by the Haftorah in which we are told, "Seek G-d while He may be found, call Him when He is near." 
The positive influences of "a day of Divine goodwill" are especially manifest on the Fast of Gedaliah because it is observed during the Ten Days of Teshuvah.
This period is the time at which the Thirteen Attributes of Mercy were revealed,  as alluded to in the verse, "Seek G-d while He may be found...."
Our Sages  offer two interpretations of this verse:
In one, the verse is understood to refer to the Ten Days of Teshuvah, a time when G-d makes Himself especially accessible to man.
The second interpretation links the verse to communal prayer.
When a community prays together, the virtue of their unity causes G-d to draw close to man.
Our Sages state that, during the Ten Days of Teshuvah, an individual's prayer can have the same power as communal prayer.
When an entire community prays together during the Ten Days of Teshuvah, their prayers reach an even higher level. 
By the same token, the positive influences of communal fasting are enhanced on the Fast of Gedaliah, because this fast is observed during the Ten Days of Teshuvah.
Aspiring to Redemption
The unbounded positive influence of a communal fast is linked to the era when goodness will spread throughout the world, the Era of the Redemption.
This may be seen in the Haftorah recited on a fast day which concludes with prophecies to be fulfilled with Redemption, among them: "And My house will be called a house of prayer for all nations." 
In the Era of the Redemption, the positive aspects of the communal fasts will be revealed because all the [commemorative] fast days will then be nullified, and, ultimately, these days will be transformed  into days of rejoicing and celebration. 
The Fast of Gedaliah, in particular, is linked to the Era of the Redemption by the identity of the person for whom the fast is named, Gedaliah ben Achikam, the governor appointed by the Babylonians after their conquest of Eretz Yisrael.
According to some opinions, Gedaliah stemmed from the House of David  and was the last member of that royal family who commanded authority over Eretz Yisrael.
This links this "day of Divine goodwill" with "the scion of David,"  Mashiach, who will restore the Davidic dynasty. 
The Fast of Gedaliah is also connected with the Redemption by virtue of the meaning of Gedaliah's name.
The Hebrew letters of Gedalyahu  form the words Gadol Yud-He, "G-d is great."
It is during the Era of the Redemption that G-d's greatness will be manifest throughout the world. 
The mention of Gedaliah in the name of the fast highlights the positive aspects of this day in yet another way.
The other three fasts connected with the destruction of Jerusalem and the Beis HaMikdash are named by the Hebrew dates on which the respective calamities occurred. The name of this fast, however, recalls a righteous Jewish leader.
"May it Be Nullified Entirely"
There is another aspect of the Fast of Gedaliah that relates to the Era of the Redemption.
This fast was instituted because the tragic assassination of Gedaliah extinguished the last embers of Jewish sovereignty in Eretz Yisrael after the destruction of the First Beis HaMikdash.
According to many commentaries,  this actually took place on Rosh HaShanah. The commemoration of the tragedy was postponed, however, so as not to conflict with the festive celebration of Rosh HaShanah, a day when we should "partake of delicacies and drink sweet beverages." 
With regard to the postponement of a fast day, there is a Talmudic opinion  that "Once [the commemoration of a communal fast] has been postponed, it should be postponed [indefinitely, i.e., cancelled]."
Understood literally, this statement expresses the minority opinion that when a communal fast falls on Shabbos, the observance of the fast should not merely be postponed until Sunday (which is the halachah as we practice it), but that there is no need to fast at all.
However, the Hebrew wording of this expression leaves room for an extended interpretation, "Once it has been postponed, may it be utterly cancelled." I.e., a postponed fast is a time when there is a greater potential for bringing about the redemptive era during which the misfortunes recalled by the communal fasts will be nullified entirely.
The fact that the commemoration of the Fast of Gedaliah is always postponed,  indicates that this day is uniquely empowered to hasten the coming of the Era of the Redemption, when all the commemorative fasts will be transformed into "days of rejoicing and celebration." May this take place in the immediate future.
- Yeshayahu 58:5; see the explanation in Tanya, Iggeres HaTeshuvah, ch. 2.
- Yeshayahu 55:6.
- See Zohar II, 177a.
- Or HaTorah, Shir HaShirim, p. 1462. This concept is alluded to in the use of the plural form of the word "seek." This can be interpreted to mean that "while G-d is to be found," i.e., during the Ten Days of Teshuvah, we should seek Him as a united community.
- Yeshayahu 56:7.
- The transformation of these communal fasts depends on teshuvah, which transforms evil into good.
Teshuvah is not bounded by time. Therefore on the communal fasts, our people are able to atone for misdeeds committed in previous generations, even those, like the assassination of Gedaliah, which were carried out in the distant past.
- . Rambam, Mishneh Torah, the conclusion of Hilchos Taaniyos, based on Zechariah 8:19.
- There are some indications that Gedaliah was related to the House of David, for it was a Babylonian custom to appoint relatives of the kings as governors. Even according to the authorities (Radak and Abarbanel to II Melachim 25:25), who state that Gedaliah was not related to the House of David, his murder shares a connection with that dynasty. Yishmael, the son of Nesanyah, was a descendant of the House of David. Jealous that Gedaliah and not he, had been appointed as governor, Yishmael murdered him. See Sefer HaSichos, 5751, p. 23.
- Daily liturgy.
- See Rambam, Mishneh Torah, Hilchos Melachim 11:1.
- In Yirmeyahu and II Melachim, Gedaliah's name is sometimes written as Gedaliah (e.g., Yirmeyahu 40:5) and other times as Gedalyahu (e.g., Yirmeyahu 40:11).
- See Rashi's commentary to Tehillim 48:2.
- See the gloss of Radak to Yirmeyahu 40:1.
- Nechemiah 8:10.
- Megillah 5b. See Likkutei Sichos, Vol. XXXIII, the Seventeenth of Tammuz, 5748.
- Moreover, Rosh HaShanah often falls on Thursday. In those years, the third of Tishrei, the day when the Fast of Gedaliah is usually commemorated, falls on Shabbos, and the fast is postponed further. Thus when the Fast of Gedaliah falls on Shabbos, the day is an even more potent catalyst for the Era of the Redemption.