Distraction [היסח הדעת ]
6. Not to get distracted. The Kohanim may not lose focus of the bracha during Birkas Kohanim. Thus, they may not look around; their faces should be downward, as if standing in Shemoneh Esrei (שו''ע סכ''ג ). Similarly, the tzibbur getting the bracha must have kavana during the bracha. Thus, they should not look at the Kohanim’s faces or hands, and certainly not somewhere else. They should just stand and focus on the bracha (מ''ב סקפ''ח ).
Kohanim
7. Covering their faces. The minhag is for the Kohanim to cover their faces with a tallis during Birkas Kohanim to make it easier not to get distracted (שו''ע ורמ''א סכ''ג ). Additionally, it is because the tzibbur getting the bracha must pay attention to the bracha and not get distracted (above, 6), so the Kohanim cover themselves so that the tzibbur cannot look at them.
8. Covering their hands. In the times of the Beis HaMikdash, when the Kohanim would use the Shem HaMeforash in the bracha, it was assur to even glance at the Kohanim because the Shechina rested on their hands. Nowadays, though, that they do not use the Shem HaMeforash and the Shechina does not rest on them, that is not a reason not to look at the Kohanim. However, the minhag today is not to look at them at all as a remembrance to the Beis HaMikdash (מ''ב סקפ''ט ). Some are also careful about this today for the honor of the Shechina (כף החיים אות ק''מ ע''פ זוה''ק ).
9. Hands out. Some Kohanim cover their faces with the tallis but leave their hands out of the tallis, as the Kohanim should not look at their own hands either, and this way they cannot see their hands (רמ''א סכ''ג ). However, this also might lead a Yisroel to look at the Kohanim’s hands. Thus, the minhag is for the tzibbur to also cover their faces with a tallis so as not to look at the Kohanim’s hands which are outside their talleisim (דרכ''מ, מ''ב סקפ''ט ). This is not a chiyuv, though, as some people in the tzibbur do not have talleisim, but it is still a good thing to do (אג''מ או''ח ח''ה סי' כ''ד אות ד'). Some people bring their children under their talleisim so that they should also not look at the Kohanim during the bracha.
10. Hands in. Other Kohanim cover both their faces and their hands with their talleisim. This is the minhag in all places nowadays. The purpose is to prevent the tzibbur from getting distracted by looking at the Kohanim’s hands (above, 6) and to remember the Beis HaMikdash (10). However, the Kohanim must be careful not to look at their own hands during Birkas Kohanim so they do not get distracted (מ''ב סקפ''ט ).
11. When the Kohanim’s hands are under talleisim, it is not so necessary for the tzibbur to cover themselves with talleisim, as the Kohanim are fully covered. Nonetheless, some still cover themselves with talleisim. This helps prevent them from looking around and getting distracted by other things (יפה ללב סל''ד, כף החיים אות קמ''ב, מקור חיים לחות יאיר ).
12. Kohen with blemishes. A Kohen with blemishes ל"ע or something unusual on him should not do Birkas Kohanim out of concern people might look at him and lose focus of Birkas Kohanim (שו''ע ס''ל ). However, if he covers his face and hands with a tallis, he may do Birkas Kohanim despite the blemishes, as people cannot get distracted by seeing him (שו''ע סל''א ).
13. Kohen without a tallis. A Kohen without a tallis should not do Birkas Kohanim. Since the accepted minhag is for a Kohen to cover himself in a tallis, it would be unusual for a Kohen to not be covered in a tallis and hence a distraction to the tzibbur. Thus, he should go out of the shul before רצה so he does not become obligated to do Birkas Kohanim (מרן פוסק הדור בתשובות והנהגות ח''ב סי' ק''ז, מו''ר בשו''ת שבט הקהתי ח''א סי' ע''ט ).