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:

"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.