There is a positive biblical commandment for kohanim to bless the nation of Israel, as it is written: “God spoke to Moshe, saying: Speak to Aharon and his sons, saying: This is how you shall bless the Israelites. Say to them: May the Lord bless you and guard you. May the Lord make His face shine on you and be gracious to you. May the Lord turn His face toward you and grant you peace” (Bamidbar 6:22-26).
In this blessing, called Birkat Kohanim, we learn to notice the basic fact that God is the bestower of blessing upon us, and our daily receptivity to Birkat Kohanim implants this faith in our hearts (Moreh Nevukhim 3:44; Ha-akeida §74). The blessing bestowed on us by God is linked to our own efforts, or, in kabbalistic terminology, to the “awakening” of the nether worlds (“itaruta de-letata”), which in turn causes the awakening of the upper realms (“itaruta de-le’eila”). By fulfilling the mitzva of Birkat Kohanim, God’s desire to bestow blessing upon Israel is awakened.
During Temple times, Birkat Kohanim would take place after the daily sacrificial offerings were completed. The Torah recounts that on the eighth day of the Mishkan’s dedication, the day that the kohanim were inaugurated in their service: “Aharon lifted his hands toward the people and blessed them. He then descended from [the altar where he] had prepared sin offering, burnt offering, and peace offering” (Vayikra 9:22). It is from here that we derive that Birkat Kohanim (also called “Nesi’at Kapayim” – “the lifting of the hands” – after this verse) took place at the conclusion of the sacrificial offerings. The reason for this is that after offering the sacrifices, which express our willingness to surrender and sacrifice ourselves for God, we are worthy of receiving His blessing.
Outside of the Temple, the Sages ordained that Birkat Kohanim is recited at the time of prayer, since prayer corresponds to offerings and is designed for the same purpose: coming closer to God. Thus, just as Birkat Kohanim takes place after the korbanot, so too it was instituted toward the end of Ĥazarat Ha-shatz of Shemoneh.