Question:
Who or what are the 36 holy people? I get the gist of such people being alive at one time, but are they still around? What is their purpose? Is it all a mystery?
Response:
Our holy books say that every generation actually has a minimum (there may be more) of 72 holy men, 36 who live in Israel, and 36 who live outside of Israel.
The number 36 corresponds to the 6 days of creation, and the 30 days of an average month. It also corresponds to the 36 candles kindled during Hanukkah.
The primary source for this teaching is in the Talmud, Succah 45b:
__________________________________________________________________________
__________________________________________________________________________
And Ḥizkiya said that Rabbi Yirmeya said in the name of Rabbi Shimon ben Yoḥai: I am able to absolve the entire world from judgment for sins committed from the day I was created until now. The merit that he accrued through his righteousness and the suffering that he endured atone for the sins of the entire world. And were the merit accrued by Eliezer, my son, calculated along with my own, we would absolve the world from judgment for sins committed from the day that the world was created until now. And were the merit accrued by the righteous king, Jotham ben Uzziah, calculated with our own, we would absolve the world from judgment for sins committed from the day that the world was created until its end. The righteousness of these three serves as a counterbalance to all the evil deeds committed throughout the generations, and it validates the ongoing existence of the world.

ואמר חזקיה א"ר ירמיה משום רשב"י ראיתי בני עלייה והן מועטין אם אלף הן אני ובני מהן אם מאה הם אני ובני מהן אם שנים הן אני ובני הן ומי זוטרי כולי האי והא אמר רבא תמני סרי אלפי דרא הוה דקמיה קודשא בריך הוא שנאמר (יחזקאל מח, לה) סביב שמנה עשר אלף ל"ק הא דמסתכלי באספקלריא המאירה הא דלא מסתכלי באספקלריא המאירה
And Ḥizkiya said that Rabbi Yirmeya said in the name of Rabbi Shimon ben Yoḥai: I have seen members of the caste of the spiritually prominent, who are truly righteous, and they are few. If they number one thousand, I and my son are among them. If they number one hundred, I and my son are among them; and if they number two, I and my son are they. The Gemara asks: Are they so few? But didn’t Rava say: There are eighteen thousand righteous individuals in a row before the Holy One, Blessed be He, as it is stated: “Surrounding are eighteen thousand” (Ezekiel 48:35)? Apparently, the righteous are numerous. The Gemara answers: This is not difficult. This statement of Rabbi Shimon ben Yoḥai is referring to the very few who view the Divine Presence through a bright, mirror-like partition, while that statement of Rava is referring to those who do not view the Divine Presence through a bright partition.
The Gemara asks further: And are those who view the Divine Presence through a bright partition so few? But didn’t Abaye say: The world has no fewer than thirty-six righteous people in each generation who greet the Divine Presence every day, as it is stated: “Happy are all they that wait for Him [lo]” (Isaiah 30:18)? The numerological value of lo, spelled lamed vav, is thirty-six, alluding to the fact that there are at least thirty-six full-fledged righteous individuals in each generation. The Gemara answers: This is not difficult. This statement of Abaye is referring to those who enter to greet the Divine Presence by requesting and being granted permission, while that statement of Rabbi Shimon ben Yoḥai is referring to those who enter even without requesting permission, for whom the gates of Heaven are open at all times. They are very few indeed.
______________________________________________ 
"The world never has less than thirty-six righteous men who receive the Divine Presence every day, for it is said, 'Happy are they that wait lo [for Him]' and the numerical value of 'lo' is thirty-six."
In merit of these righteous individuals, our world receives the divine vitality that keeps it going. We do not know for sure, however, the identity of all these extraordinary individuals.

Sources
The 36 hidden tzadikim, also known as the Lamed Vovniks, are discussed by the Tikunei Zohar (50b), Sfat Emet, Meor V'Shemesh and others. The Meor V'Shemesh explains that the number 72 corresponds to the 70 Elders, plus Moses and Aaron. The Sfat Emet mentions the relationship with the Chanukah candles in his discussion of Chanukah.