The three crowns draw Heavenly light

בגמרא ומדרש תרומה.

In the Gemara and the Midrash on [Parshas] Terumah.

The Sefas Emes draws on the teaching of Chazal concerning the crowns of the Mishkan's vessels.

שלשה זרים זר בארון ושולחן ומזבח.

There are three crowns [zeirim]: a crown upon the Aron (Ark), the Shulchan (Table), and the Mizbe'ach (Altar).

Three of the Mishkan's vessels bore a golden rim or crown — the Ark, the Table, and the Altar.

כתר תורה וכהונה ומלכות.

[These correspond to] the crown of Torah, of Kehunah (priesthood), and of Malchus (kingship).

The three crowns represent the three crowns of Klal Yisrael: Torah (the Aron), Kehunah (the Mizbe'ach), and Malchus (the Shulchan).

והובא ברש"י.

And this is brought in Rashi.

Rashi cites this teaching of the three crowns in his commentary.

והענין הוא שכל אלו הם מעוררין וממשיכין עזר וסיוע מעולם העליון שהכהן יש לו כח לעורר בעולמות עליונים ע"י עבודה שלו.

And the idea is that all of these arouse and draw down help and assistance from the upper world: for the Kohen has the power to arouse [influence] in the upper worlds through his avodah.

Each of the three crowns channels Divine assistance from above into this world; the Kohen does so through his service in the Bais Hamikdash.

וכמו כן מלך ישראל.

And likewise the king of Yisrael.

The Jewish king, crown of Malchus, similarly draws down Heavenly help to the nation.

וכמו כן ת"ח העוסקים בתורה לשם שמים.

And likewise the talmidei chachamim who engage in Torah for the sake of Heaven.

Torah scholars who learn lishmah, bearing the crown of Torah, also draw spiritual influence from above.

וזה פי' הכתר שהוא אור מקיף ומאיר למעלה מכפי מדריגת גוף האדם.

And this is the meaning of the "crown" — that it is an encompassing light (or makif) that shines from above, beyond the level of a person's physical body.

A crown sits above the head, symbolizing an "or makif," a surrounding light that transcends a person's bodily, finite level.

וזהו המדריגה שניתן לבנ"י שמיוחדין מכל האומות עובדי האלילים כ) שיכולין להמשיך כח מעולם העליון.

And this is the level given to Bnei Yisrael, who are distinguished from all the idol-worshiping nations, that they are able to draw down power from the upper world.

This capacity to draw down Heavenly influence sets Bnei Yisrael apart from the idolatrous nations and defines their unique spiritual standing.

וז"ש ואתם תהיו לי ממלכת כהנים הוא כתר מלכות וכהונה.

And this is the meaning of "And you shall be to Me a kingdom of priests" (Shemos 19:6) — this is the crown of Malchus and Kehunah.

"A kingdom of priests" alludes to two of the crowns — kingship and priesthood — that Bnei Yisrael bear.

וגוי קדוש מרומז על התורה שהוא קודש:

And "a holy nation" alludes to Torah, which is holiness.

The phrase "a holy nation" hints at the third crown — the crown of Torah, which is the source of kedushah.

Summary: The three golden crowns on the Aron, Shulchan, and Mizbe'ach correspond to the crowns of Torah, Malchus, and Kehunah — each an "or makif," an encompassing light by which Bnei Yisrael draw Divine power from the upper world. This unique capacity, denied to the idolatrous nations, is what the verse means by calling Yisrael "a kingdom of priests and a holy nation."