Mutual Oath
“Shavuot” comes from the word “shevua” (oath). On the day the Torah was given, G-d and the Assembly of Israel swore a mutual oath. We swore to the Master of the Universe that we would never exchange Him, G-d forbid, for other gods; and G-d swore to us that He would never exchange us for another nation.
(Ohr HaChaim HaKadosh)
Without Torah – a Desert
The Israelites received the Torah in the desert because man (in Hebrew, adam) is named after the earth (in Hebrew, adamah). A person without Torah is like a barren desert with no grass or vegetation. Therefore, the Torah was given to him – to complete him – so that this “earth” can bring forth trees and good plants.
(The Maharal of Prague)
Refining the Lowliest
"...and they stood at the bottom of the mountain." (Exodus 19:17) Specifically at the bottom of the mountain. This teaches us that the purpose of the giving of the Torah is for man to refine the physical world and make a dwelling for G-d in the lowest realms.
(the Rebbe)
Giving and Receiving
Shavuot is called, “The Time of the Giving of Our Torah,” not “The Time of the Receiving of Our Torah.” The giving of the Torah was equal for all of Israel. But the receiving of the Torah is not the same for every individual; each person receives it according to their level and understanding.
(Rabbi Menachem Mendel of Kotzk)