The priestly blessing is found in Numbers 6:23-27. Traditionally, the priests blessed the people every morning after the sacrifice at the Temple. Today, many synagogues end their service with this blessing as a benediction.
When recited, the kohen (priest) raises his hands with the palms facing outward and the thumbs of his outspread hands touching. The four fingers on each hand are split into two sets of two fingers each (thus forming the letter Shin, an emblem for Shaddai=God Almighty).
Note that the Lord does not command the kohanim (priests) to bless the people using their own words, but rather provides the exact formulation for the blessing, prefacing the instruction with the words: "Thus shall you bless." This reveals that the blessing comees from the Lord himself, and the priests are but the means for transmitting his gracious will. This is further indicated by the verse that immediately follows the birkat kohanim: "So shall they put my name upon the people of Israel, and I will bless them" (Num 6:27).
In the blessing that follows, the text is said (in an undertone) in response to the priest's recitation:
May the Lord bless you and protect you. May it be his will.
May the Lord shine his face upon you and be gracious to you.
May the Lord turn his countenance to you and give you peace.
Orthodox Jews do not look at the Kohanim while they are saying the blessing. They should look at the ground and concentrate on the blessing and because the Divine Presence will be shining upon the fingers making the sign and out of respect for God, no human should look upon the hands.