What is a "hidden yom tov"?

Question

I sometimes hear mention of certain days being called a "hidden yom tov." Examples include Rosh Chodesh, Hoshana Rabba and Erev Yom Kippur.

I have a few questions related to this:

• What does it mean that a day is a hidden yom tov, and what is the purpose?
• What is the source of this concept, and how do we know what days these are?
• What are all of the days that we know are hidden yamim tovim, and might there be additional days that we don't know about?
• Will there come a time when hidden yamim tovim are "revealed"? What will be different then?

Answer 1

A start of an answer - predominantly aimed at answering @ninamag

It writes Tehillim 81:4

תִּקְע֣וּ בַחֹ֣דֶשׁ שׁוֹפָ֑ר בַּ֝כֵּ֗סֶה לְי֣וֹם חַגֵּֽנוּ

Blow the shofar on the new moon, at the appointed time for our festival day.

As @ninamag asserts the word "בַּ֝כֵּ֗סֶה" in this context means appointed (as explained by Rashi, the Malbim Biur Hamilos, Radak and Metzudas Dovid). However, it is worth noting the Ibn Ezra who explains that the choice of wording is such because:

וטעם בכסה – שהלבנה מתכסה בו והנה כן משפט כל חדש

And the explanation of "בכסה" is that the moon is concealed on that day and that is the rule for every new moon.

The Gemara in Rosh Hashanah 8a - 8b explains likewise:

מִמַּאי דְּתִשְׁרִי הוּא? דִּכְתִיב: ״תִּקְעוּ בַחֹדֶשׁ שׁוֹפָר בַּכֵּסֶה לְיוֹם חַגֵּנוּ״, אֵיזֶהוּ חַגשֶׁהַחֹדֶשׁ מִתְכַּסֶּה בּוֹ — הֱוֵי אוֹמֵר זֶה רֹאשׁ הַשָּׁנָה. וּכְתִיב: ״כִּי חֹק לְיִשְׂרָאֵל הוּא מִשְׁפָּט לֵאלֹהֵי יַעֲקֹב״

The Gemara raises a question: From where is it known that the day of judgment is in Tishrei? As it is written: “Blow a shofar at the New Moon, at the covered time for our Festival day” (Psalms 81:4). Which is the Festival day on which the moon is covered, i.e., hidden? You must say that this is Rosh HaShana, which is the only Festival that occurs at the beginning of a month, when the moon cannot be seen. And it is written in the next verse: “For this is a statute for Israel, a judgment of the God of Jacob” (Psalms 81:5), implying that this is the day of judgment. (Sefaria translation and notation)

Simply put, all other Jewish holidays occur later in the month, when most of the moon is visible. Only Rosh Hashanah occurs at the very beginning of the month when the moon is still covered.

With this in mind, perhaps that's why Rosh Chodesh, as mentioned in the question, is regarded as a hidden yom tov as it is at a time when the moon is hidden.

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EDIT

(In addition to the above, I am reminded of the minhag that some people have to eat kreplach in their soup on some of the days you suggest in the question, the idea being that just like the meat is not visible from the outside, it is appropriate for the "hidden" nature of the day. (Not yet seen it officially in a source). I know people who have the custom to have them on erev Yom Kippur, Hoshanah Rabba and Purim. I imagine possibly with the first two instances; it may well lie with the fact that we are all undergoing an intense judgement period that only G-d knows the outcome of. Yom Kippur being the day in which our judgement is sealed and Hoshanah Rabbah when it is "posted" and thus there are those who eat Kreplach as nod to this concealed and hidden nature of the day. Similarly, Purim is known as a story that was full of hester panim and so is likewise appropriate to partake of the kreplach custom.)

As far as Yom Kippur - in the answer here the Bnei Yissascher, cheilek 2, maamar 8, os 2 (last paragraph) when speaking about why masechta Yoma is so-called and is not more specific to the day of Yom Kippur it writes:

והנה תמצא גם בתורה שבעל פה, המסכתא המדברת מענין מצות היום לא נקרא שמה על שם היום יום הכיפורים (כאינך שבת, פסחים, ראש השנה, סוכה) רק נקרא יומא, להורות קדושת היום הוא ממקום נעלם ראוי להסתירו, על כן מנהג אנשי מעשה שלא להזכיר שמו כל כך בפשיטות באיזה דברים, רק כשמזכירים מענינו לאיזה הצטרכות קוראים אותו סתם יום הקודש ודי בזה למשכיל (עיין ברכה משולשת פתיחה למסכת יומא)

And behold you find also with the Torah Sheba'al Peh (Oral Law), the tractate speak about the specific mitzvah of the day, yet it (masechta yoma) is not named after the day Yom Kippur (not like Shabbos, Pesachim, Rosh Hashanah, Succah) rather only it is called 'Yoma'? To teach you that the sanctity of the day is from a hidden place and is fitting to be concealed, therefore people of deeds don't mention its name as in the simple understanding, rather it is only when we are reminded of the subject matter and for what need it is called, that is just the Holy Day and that is enough to understand (Refer to the Bracha meshuleshes, in the introduction to masechta yoma).