Shavuos unites Yisrael under Hashem's kingship

חז"ל קראו לזה החג עצרת.

Chazal called this festival "Atzeres."

The Sefas Emes notes that the Sages refer to Shavuos by the name "Atzeres," and he will unpack what this name conveys.

ובתורה נקרא יום הקהל.

And in the Torah it is called "the day of assembly (Yom HaKahal)."

The Torah associates the giving of the Torah with the day of gathering, "Yom HaKahal" — the day the people were assembled at Sinai.

כי בקבלת התורה הי' לבנ"י לב אחד כמ"ש הקהל לי את העם והיינו כניסי' לשם שמים וסופה להתקיים שנשאר מזה כח בכל חג השבועות להתאסף בכלל ובפרט נפשות בנ"י.

For at the receiving of the Torah, Bnei Yisrael had "one heart," as it is written, "Assemble the people for Me" (Devarim 4:10) — and this was a gathering for the sake of Heaven, which is "destined to endure" (cf. Avos 4:11); for there remains from it a power, every Shavuos, for the souls of Bnei Yisrael to be gathered together, both as a whole and individually.

At Sinai the nation became "k'ish echad b'lev echad," united with one heart. Because that assembly was purely l'shem Shomayim, it is a gathering "destined to endure" — and its power returns each Shavuos, drawing the neshamos of Bnei Yisrael together collectively and uniting each person's own inner faculties as well.

ובאמת גם בכל יום מתעורר כח מתן תורה והוא ק"ש שמע ישראל שהוא התאספות כלל ישראל.

And in truth, every day too the power of Mattan Torah (the giving of the Torah) is awakened, and that is Krias Shema — "Shema Yisrael" — which is the gathering together of all of Yisrael.

This unifying force is not limited to Shavuos; it is renewed daily through Krias Shema, whose very words "Shema Yisrael" call the entire Klal Yisrael into one assembly.

כי עצרת ג"כ מלשון מלכות כמו זה יעצור בעמי שע"י שמקבלין מצות המלך נעשין אגודה אחת לעשות רצונו ית"ש שזה הי' בקבלת התורה קבלת עוז מלכות שמים ועול מצות ובזה נעשין בנ"י אחדות אחד זהו שמע ישראל:

For "Atzeres" also has the connotation of malchus (kingship), as in "this one shall rule (yaatzor) over My people" (Shmuel I 9:17) — for by accepting the commands of the King, they become one bound bundle (agudah achas) to do His will, may He be blessed; and this is what happened at the receiving of the Torah, the acceptance of the might of malchus Shomayim and the yoke of mitzvos, and through this Bnei Yisrael become a single unity — this is "Shema Yisrael."

The word "Atzeres" also bears the sense of kingship and rule. When Bnei Yisrael accept the King's commands they bind themselves into one "agudah achas" to fulfill His ratzon. That is exactly what occurred at Sinai — receiving ol malchus Shomayim and ol mitzvos — and it is what we renew when we declare "Shema Yisrael, Hashem Echad," making ourselves one in accepting His Oneness.

Summary: Shavuos is called "Atzeres" and "Yom HaKahal" because at Mattan Torah Bnei Yisrael became "one heart," a gathering purely for the sake of Heaven that is destined to endure. Its unifying power returns each Shavuos and, indeed, every day through Krias Shema. "Atzeres" also connotes malchus: by accepting the King's mitzvos and the yoke of His kingship, Bnei Yisrael are bound into a single agudah to do His will — and this unity is the essence of "Shema Yisrael."