Q. Some people seem to turn their backs on the Kohanim during the priestly blessing. Why?
The sages explain that this applied only at the time of the Temple, when the kohanim used the Shem HaM’forash – the authentic, sacred name of God. It was believed that the Divine Presence streamed through the open fingers of the priests, and to gaze directly at the priests at this moment bordered upon irreverence.
In the Jerusalem Talmud (Megillah 4:8) the problem is explained differently, i.e. that people might be more intent on looking at the kohanim than focussing on the words and meaning of the blessing.
As codified in the Shulchan Aruch, the law is, “When the kohanim bless the people, the latter should concentrate on the blessing with their faces towards the kohanim but without looking directly at them” (Orach Chayyim 128:23).