After the rebellion of Korach, the Torah reinforces the special status of the tribe of Levi and the Kohanim. It will be their responsibility to ensure that all the tasks in the Mishkan are performed correctly, and that the sanctity of the Mishkan is maintained:
And Hashem said to Aharon, “You and your sons and your father’s house with you will bear the transgression of the Sanctuary, and you and your sons with you shall bear the transgression of your priesthood. And also draw near with you your brethren the tribe of Levi, your father’s tribe, that they be joined to you and minister to you. And you and your sons with you shall be before the Tent of Testimony. And they will safeguard your watch and the watch of the entire Tent; however they will not approach the holy utensils or the altar, lest they die, both they and you. And they shall be joined to you, and safeguard the watch of the Tent of Meeting for all the worship of the Tent; and the layman shall not approach you. And you shall safeguard the watch of holiness and the watch of the altar, so that there will no longer be wrath against the Children of Israel” (Bamidbar 18:1-5).

The Sages teach that in the last two verses — and safeguard the watch of the Tent of Meeting and you shall safeguard the watch of holiness — there are two mitzvot, one positive and one negative (Mechilta; Sifre Zuta 292 l. 9; Midrash HaGadol). Sefer HaChinuch (ascribed to either R. Aharon HaLevi or R. Pinchas HaLevi of Barcelona, mid-13th Century) writes:
• Commandment 388: that the Kohanim and Leviim are commanded to guard the Sanctuary and walk about it continually, every single night, the entire night … the Kohanim within, and the Leviim without.
• Commandment 391: not to stop the guarding of the Sanctuary.

As Rambam explains (Laws of the Temple, chapter 8), there were 24 sentry posts throughout the Temple precincts, 3 manned by Kohanim and 21 by Leviim. An additional guard, called the “Man of the Temple Mount,” circulated among the 24 posts to verify that the guards were awake. As he approached, the guard was required to greet the Man of the Temple Mount with the words, “Peace unto you!” If the guard did not do so, the man was permitted to strike him with his stick to rouse him, or even to set fire to his clothing if he had fallen asleep!

Although the above passage is cited as the source of these commandments, these concepts have been heard before. When the camp was first set up, we were informed (at the beginning of the book of Bamidbar) of the Levites’ role in guarding the Sanctuary. On the four sides of the Mishkan, between it and the other tribes, the Levites encamped in four divisions. To the west was the division of Gershon; to the south was the division of Kehat; to the north was the division of Merari:
And those who encamp before the Mishkan to the front, before the Tent of Meeting on the east, were Moshe and Aharon and his sons; they keep the watch of the Sanctuary for the watch of the Children of Israel. And the layman who approaches shall be put to death (3:38).

What is the purpose of this guarding? Certainly, it was not for security, as Rambam says (loc. cit., par. 1):
There is no fear there of either enemies or of bandits.

In the view of Ibn Ezra (on 3:38), all the Leviim are encamped around the Mishkan — and in particular Moshe, Aharon and the Kohanim are positioned in front of the entrance to the Mishkan — to safeguard the Mishkan against wrongful entry by anyone unqualified. The watch of the Sanctuary is for the protection of the Sanctuary from transgression, not from danger.

Rambam, quoting the Midrash (Sifre Zuta, loc. cit., l. 10-11), gives a different reason for the guarding:
Its guarding is nothing but honor for it. There is no comparison between a palace that has sentries about it and a palace without sentries.
Sefer HaChinuch concurs that the guarding confers honor and distinction on the Sanctuary.

Another perspective is found in Likutei Anshei Shem to 3:38. He cites a central concept from the Kabbalah, that a “bestirring from below” (itaruta diletata) gives rise to a “bestirring from above” (itaruta dile’eila). This means that our behavior in the human realm is utilized by Hashem to bestow His beneficence upon the universe. Every small act of sanctification, therefore, sets a process in motion of cosmic magnitude.

An example of this can be found in the very beginning of the Turei Zahav (commentary on the Shulchan Aruch by R. David ben Shmuel Halevi of Lvov, 1586-1667). There, the Shulchan Aruch, writing of the importance of a person’s awaking with alacrity to serve the Creator, says, “he should awaken the dawn.” The Turei Zahav explains this means that he should arouse himself first from within and then the arousal from Above will follow; this initial internal motivation is greater than when the motivation comes from without.

The same is true, says Likutei Anshei Shem, of the guarding in the Temple:
“As a result of their guarding, when they remain awake and oversee the Mishkan from below, accordingly Hashem will also watch over them to guard the world, that no misfortune befall them.”
They keep the watch of the Sanctuary for the watch of the Children of Israel… And they safeguard the watch of the Tent of Meeting … so that there will no longer be wrath against the Children of Israel. The guarding in the Sanctuary by the Leviim effectuates the protection of the world by Hashem.
When we awaken to Hashem, He awakens to us.
(I would like once again to thank R. David Avraham Spektor of Bet Shemesh for directing me to these sources.)