We learned that Rabbi Yosi said that when the priest raises his hands [to bless the congregation], the people must not look at him [at his fingers], since the Shechinah rests on his hands [his 10 fingers allude to the 10 Sefirot and they are a throne on which the Shechinah rests]. Rabbi Yitzhak asked — even so, if they cannot see [the Shechinah], what harm is there for them [if they look at the fingers of the priest]? It is because it is written: "For no man shall see Me, and live." (Ex. 33:20) [Our Sages explained:] It is only during their lifetime that they cannot see. At their death, they do see. He [Rabbi Yosi] told him [Rabbi Yitzhak]: It is because the Holy Name is alluded to in the fingers of their hands [meaning the 10 fingers allude to the 10 sefirot which are the Holy Names], and a person should have awe. Although they cannot see the Shechinah, they should not look at the hands of the priests, so the people should not be impudent towards the Shechinah. [One must consider this as if he could see the Shechinah with one's eyes, and therefore be awed and not impudent.]

Although they cannot see the Shechinah, they should not...be impudent...

We learned that when the priest raises his hands in blessing, the people must be in awe and fear, and know that at that time a time of goodwill/et ratzon prevails throughout the worlds, the upper and lower beings are blessed and there is no judgment among them all. That is the time when the most ancient and concealed [Arich Anpin] is revealed [and illuminates] in Zeir Anpin and peace prevails in all [the worlds, which explains why the last words of the blessing are: “and give you peace”].

Rabbi Shimon said: these three verses [that comprise the priestly blessing], all begin with yud, yud, yud, Yevarechecha ['bless you'] , Ya'er ['shine upon'] and Yisa ['lift up']. They all show the perfect faith, that whoever needs [including Abba and Imma] will be blessed from Atika: yud, yud, yud, [3 times, showing that Atika's blessings are sourced in the three groups of “white hair” or complete mercy, represented by the three expansions of Havaya with yud's, each having a gematria of 72 that equals kindness/chesed]; Zeir Anpin shall be blessed from [Above by] the most Ancient [Arich Anpin, because Zeir Anpin now, during the priestly blessing, receives the Divine flow direct from Arich Anpin and not in the usual way of it devolving down to Zeir Anpin through Abba and Imma]. Therefore, "G‑d bless You" Above [Zeir Anpin shall be blessed from Arich Anpin] "And keep you" is below [for after Zeir Anpin receives flow, it is drawn down below into the physical world] and so in the same manner from each [of the other verses of the priestly blessing].

...judgment will turn into mercy for him.

And a Tanna learned from Rabbi Shimon that whoever is distressed from his dream [because he had a bad dream] shall come when the priests spread out their hands [in blessing], and say: "Master of the universe, I am Yours and my dreams are Yours..." [as written in many prayer books] What is the reason [for this at the time of the priestly blessing]? It is because compassion prevails in all the worlds at that time. Whoever will put forth his prayers about his distress, judgment will turn into mercy for him [because the priestly blessings draw down the light of compassion that will mitigate his distress].

BeRahamim LeHayyim:
One needs to see a traditional synagogue during the priestly blessing on a Festival Day to really appreciate this Zohar. During the repetition of the Amidah prayer, the Cohen's (and Kahn's, Korn's, Koren's, etc.) all leave together with the Levites [Levy, Levinson, Levine, LeVign, etc.); the latters' job is to wash the formers' hands using a vessel. When the chazan begins saying "Retzei", the kohanim slip off their shoes and come forward in front of the Ark, where they stand facing the Ark. The chazan calls out "Kohanim, Your holy people", and the kohanim, covered with a Tallit over their heads and hands, turn around and bless the congregants.

Neither the priests nor the congregation gaze at the kohanim's raised hands, for these upraised hands are the vehicle through which G‑d's blessing flows upon us —His chosen people. In fact traditional law prohibits any raising of one's hands higher than the head save for this blessing!

The melody invokes an age long-gone, and each word is said by the chazan and repeated by the kohanim. Additional prayers are said by all to take full advantage of this special moment. In some synagogues in the Holy Land, this is done daily; in others, weekly. In the Diaspora, rarely aside from on Festivals.

With this short explanation, perhaps we can understand the magnitude of the moment, and why the oh-so-important concomitant requirement of complete concentration with simultaneous avoidance of gazing. We are told that both Abel and Isaac were punished by their gazing. Moses "turned aside" when the Burning Bush revealed to him G‑d's awesome presence. For us, it is enough to learn that sometimes we shouldn't look - physically. Through one's inner vision, well, that is another story for another time.

[Bracketed annotations from Metok Midevash and Sulam commentaries]