Milah binds body to the neshamah

התהלך לפני והי' תמים.

"Walk before Me and be tamim (whole/perfect)."

Hashem commands Avraham to walk before Him and become "tamim" — the verse that introduces the mitzvah of milah (circumcision).

מה שנקרא תמים ע"י המילה ביאור הענין שיש לאדם שני כחות בעולם הזה ובעולם העליון והיינו כח הנפש בגוף וכח הנשמה שלמעלה שאינו מתפשט בגוף האדם.

That one is called tamim through the milah — the explanation is that a person has two powers, one in this world and one in the upper world: namely, the power of the nefesh within the body, and the power of the neshamah above, which does not spread into the body of the person.

The Sefas Emes explains that every person has a lower soul-force (nefesh) clothed in the body and a higher soul-force (neshamah) that remains above, never fully descending into the physical body.

וכשהאדם זוכה ומקשר עצמו לכח נשמתו נקרא תמים ובא בזכות המילה לכן נקרא ברית שמקשר ומחבר הגוף בהארת נשמתו החופפת על הגוף ובמדרש איתא כי תמה אברהם איך ע"י שיחתך אבר יהי' נקרא תמים.

When a person merits to bind himself to the power of his neshamah, he is called tamim, and this comes through the merit of milah; therefore it is called a bris (covenant), for it binds and connects the body to the radiance of his neshamah that hovers over the body. And in the Midrash it is brought that Avraham wondered: how, by cutting off a limb, would he be called tamim ("whole")?

Becoming "whole" means linking the body to the light of the higher neshamah that hovers above it; milah forges that bond, which is why it is a "bris." Avraham was puzzled: how can removing part of the flesh make a person more complete rather than less?

ובאמת ע"י חסרון זה בגוף זוכה אל השלימות כי הגוף הוא בעל חסרון וכדאיתא בזוה"ק על פסוק ה' חפץ דכאו החלי שע"י חסרון בגוף זוכה לשלימות של הנשמה.

But in truth, precisely through this deficiency in the body one merits wholeness, for the body is something deficient; as the Zohar HaKadosh brings on the verse "Hashem desired to crush him, He made him ill" — that through a deficiency in the body one merits the wholeness of the neshamah.

The resolution is that the body, left to itself, is inherently lacking; diminishing the body's dominance (through milah) is what allows the neshamah's perfection to shine through. Suffering or "lack" in the physical can be the very gateway to spiritual completeness.

ואיתא בזוה"ק בראשית ברית אש פי' שכל הבריאה ע"י התורה ובודאי כח הבריאה שבתורה הוא בהנהגה שלמעלה מהגוף והגשמיות ונקרא אש דת כלומר הנהגה אלקית וע"י התורה יכולין לקשר עוה"ז בכח חיות הקדושה שמשם שורש הכל

And the Zohar HaKadosh brings that "Bereishis" hints at "bris eish" (a covenant of fire) — meaning that all of creation came about through the Torah, and surely the creative power within the Torah lies in a mode of governance above the body and physicality, called "aish das" (the fiery law), that is, Divine governance; and through the Torah one is able to bind this world to the power of holy vitality, from which is the root of everything.

The Torah is the instrument of creation, and its creative force operates on a plane above the physical — a "fiery," Divine mode of conduct. Through Torah a person can connect even this material world back to the holy life-force that is the source of all existence.

וזה מה שהתורה מתפארת ואהי' אצלו אמון פי' שבכחה ליישר כל המעשים והברואים ולקשר אותם בכח הפנימי שלמעלה מהטבע שהרי על ידה נברא הכל מאין ליש וזהו בראשית ברית אש והתורה והמילה ענין אחד כמ"ש במדרש ע"פ מגיד דבריו ליעקב כי בלי המילה אין זוכין לתורה ע"ש:

This is what the Torah takes pride in: "I was beside Him as a nursling/craftsman (amon)" — meaning that it has the power to straighten all the deeds and creatures and to bind them to the inner power that is above nature, for through it everything was created from nothing into being. And this is "Bereishis — bris eish," and the Torah and the milah are one matter, as the Midrash says on the verse "He tells His words to Yaakov" — for without the milah one does not merit the Torah; see there.

The Torah's pride is that it can set all of creation aright and reconnect it to the inner, supernatural force through which everything was brought into being. Torah and milah are ultimately one idea — both bind the physical to the Divine — and indeed the Midrash teaches that without milah one cannot fully merit the Torah.

Summary: A person has a lower nefesh within the body and a higher neshamah hovering above it; to be "tamim" is to bind the body to that higher light. Milah accomplishes this — paradoxically, the body's "deficiency" is what opens the way to the neshamah's wholeness. Both milah and Torah are a single avodah of fastening this physical world to its supernatural, Divine root, which is why milah is a prerequisite for truly meriting the Torah.