Yom HaMeyuchas is the day between Rosh Chodesh Sivan and the Shaloshes YeMei Hagbolah
It is sandwiched between these special times - so it also is special
It also always falls out on the same day of the week as Yom Kippur, showing how special it is

The Rhiziner Rebbe explained the greatness of the day today:

A king wanted his palace decorated, so he invited four famous artists, each to paint one wall of the palace. Three of the four worked assiduously to mix the paints and sketch out the drawings that would decorate their respective walls. The fourth sat by, seemingly idle, writing numbers in a note pad. As the three were finishing their work on their individual walls, the fourth finally stood up and arranged a series of mirrors on his wall. When the king arrived to judge the work, he awarded the prize to the fourth artist. He said that while the creativity and skill of each of the three artists were both evident and special, the work of the fourth artist was truly the most beautiful in that it reflected the glory and the grandeur of all that surrounded it.

Rav Soloveitchik explains in another way:

While there is an argument between the Rabbonon and Rebbe Yosi as to whether the Torah was given on 6 Sivan or 7 Sivan, on Shavu’os, which saw klal Yisrael at Har Sinai as “Ish Echad BeLev Echad”, [one heart and unity], we don’t want to emphasize a Machlokes. Indeed there is unanimity in that, as the Gemara states, “DeKuli Alma, beShabbos Nitna Torah LeYisroel”, that all agree, that the Torah was given on a Shabbos. Chazal wanted to establish a calendar that would respect both the Rabbonon and R’ Yosi, and not emphasize their disagreement. They therefore wove both opinions into our observance. We observe Shavu’os on the 6th of Sivan in accordance with the Rabbanan who held that there were only two day of Hagbalah, but we also commemorate the THREE days of Hagbalah as stipulated by R’Yosi. By observing three days before the day of Matan Torah, they must therefore be on the 3rd, 4th, and 5th of Sivan. These three days were not the original Sheloshes Yemei Hagbalah, but they allow us to respect and honor R’Yosi’s view that there were three days, even though we do not observe Matan Torah on the 7th of Sivan, as he taught.

Therefore, the one day between Rosh Chodesh and our reconstituted Sheloshes Yemei Hagbalah is indeed a “special Meyuchasdik” day. It reminds us that Chazal developed our calendar so that there would be Shalom, by reconciling the views of the Rabbonon and R’Yosi. It is a reminder for us to try our best to eliminate Machlokes amongst Klal Yisrael- so that we can once again become united “Ke’ish Echad BeLev Echad” as we prepare to re-experience Matan Torah on Shavu’os.

Happy Yom HaMeyuchas!!