Aaron and his sons and descendants were commanded to use that blessing (Num. 6:22), and Rashi and Ibn Ezra say that in the previous verse (Lev. 9:22) that is what is meant when the text says, “And Aaron lifted up his hands towards the people and blessed them”.
Nachmanides disputes this and argues that Aaron’s blessing of the people resembled the King Solomon’s invocation when the Temple was dedicated (I Kings 8:55).
Even Rashi and Ibn Ezra would agree that though Moses was a Levite, it was Aaron who was the Kohen, so when the two brothers together blessed the people it was not in a ritual sense but in some other way.
Rashi believes that they uttered the words that conclude Psalm 90 (known as T’fillah L’Moshe, “The Prayer of Moses”), “May the graciousness of the Lord our God be upon us” – i.e. “May it be God’s will that the Sh’chinah (the Divine Presence) may rest upon the work of your hands”.
The people were apprehensive because they felt the Sh’chinah had not appeared during the seven days of consecration and thought they were still being punished for the sin of the golden calf.
Any group who embark upon a religious project ought to have similar qualms: “Will God accept our offering? Are we good enough and worthy enough to have attempted this project? Will our achievement be a monument to human ambition or an act of service to God?”
Their greatest hope and prayer must be to sense that Moses and Aaron approve of what they have done and pray for God’s approval and blessing.