The eternal mutual oath of Sinai

שבועות הוא ע"ש השבועה שנשבעין ועומדין מהר סיני.

Shavuos is named for the oath (shevuah) that we are sworn and bound by from Har Sinai.

The Sefas Emes reads "Shavuos" not only as "weeks" but as "oaths" — for at Har Sinai an enduring vow was sworn that still binds us.

וכולל ב' השבועות.

And it includes the two oaths.

The plural "Shavuos" hints at two mutual oaths sworn at Sinai.

שנשבעו בנ"י לעבוד את ה' כמ"ש ב"פ אשר דיבר ה' נעשה והן הן שבועה.

That Bnei Yisrael swore to serve Hashem, as it says twice, "all that Hashem has spoken we will do" — and these very words are an oath.

The first oath is Yisrael's: their twice-repeated declaration of "na'aseh" — "we will do" — constituted a binding vow to serve Hashem.

וכן הקב"ה נשבע לבנ"י כמ"ש ב"פ אנכי ה' אלקיך בעשרת הדיברות והוא שבועה.

And likewise the Holy One swore to Bnei Yisrael, as it says twice, "I am Hashem your God" in the Ten Commandments — and this is an oath.

The second oath is Hashem's: His own declaration of "Anochi Hashem Elokecha" in the Aseres HaDibros is, as it were, His vow to Yisrael, binding Himself to them.

וכ"כ הואיל ה' לעשות אתכם לו לעם הואיל פי' שבועה.

And so it is written, "Hashem has sworn (ho'il) to make you a people unto Himself" — "ho'il" means an oath.

The Sefas Emes brings further proof that Hashem bound Himself by oath to make Yisrael His own nation, reading the word "ho'il" as a term of swearing.

ושבועות אלו מתעוררין בחג השבועות ולשון חז"ל מושבע ועומד מהר סיני ששבועה זו קיימת לעד בכל איש ישראל ואין לה התרה עולמית:

And these oaths are awakened on Chag HaShavuos; and in the language of Chazal, "sworn and standing from Har Sinai" — for this oath endures forever in every Jew, and it has no annulment ever.

Every Shavuos these two mutual oaths are reawakened. Chazal's phrase "mushba ve'omed" expresses that the Sinai oath is permanently binding within every Jew; unlike ordinary vows, it can never be released or annulled.

Summary: Shavuos is named for the shevuah — the mutual oath sworn at Har Sinai. Two vows were exchanged: Yisrael swore "na'aseh" to serve Hashem, and Hashem swore "Anochi Hashem Elokecha" to be their God and make them His people. These oaths reawaken every Shavuos and remain eternally binding within every Jew, never to be annulled.