The S'fat Emet, Reb Yehuda Leib Alter of Gur, explains that an inner awareness occurred. The souls of everyone present at Sinai realized two items. One, that each soul was a portion of the Divine, and, two, that Hashem was present. That throughout their lives they were garbed in the natural realm, but at this instant they sensed a greater reality. Each looked inside themselves and saw the inner truth of themselves and the world.
Nature is just a veneer obscuring the actuality below.
At that special time and place there was a subtle slipping off of the veil, and all saw directly into the truth below. That the spirituality emanating from Hashem is the 'real world' and our physical realm is the ersatz. That was the revelation. Reb Nachman of Breslav says that the awe of Hashem reached a critical mass within our souls to develop an awareness of Him and one another that, in turn, generated humility. The miniature Divine Presence entered the vacuum left by our departed ego.