Why do the Cohanim hide for the blessing?

Question:

Why do the Cohanim cover themselves and their hands when they do the priestly blessing? Why do the people cover themselves in their talitot?

Answer:

The Cohanim are meant to concentrate on blessing the congregation, and the congregation should concentrate on receiving the blessing. So that the Cohanim shouldn't be distracted by looking at the people, and so that the people shouldn't be distracted by looking at the Cohanim, the Cohanim cover their faces and hands with a tallit.

Source: Shulchan Aruch Harav 128:36

Rabbi Eliezer Posner