Birkat Cohanim/ Nesiyat Cappayim
(כב) וַיְדַבֵּ֥ר יְהוָ֖ה אֶל־מֹשֶׁ֥ה לֵּאמֹֽר׃ (כג) דַּבֵּ֤ר אֶֽל־אַהֲרֹן֙ וְאֶל־בָּנָ֣יו לֵאמֹ֔ר כֹּ֥ה תְבָרֲכ֖וּ אֶת־בְּנֵ֣י יִשְׂרָאֵ֑ל אָמ֖וֹר לָהֶֽם׃ (ס) (כד) יְבָרֶכְךָ֥ יְהוָ֖ה וְיִשְׁמְרֶֽךָ׃ (ס) (כה) יָאֵ֨ר יְהוָ֧ה ׀ פָּנָ֛יו אֵלֶ֖יךָ וִֽיחֻנֶּֽךָּ׃ (ס) (כו) יִשָּׂ֨א יְהוָ֤ה ׀ פָּנָיו֙ אֵלֶ֔יךָ וְיָשֵׂ֥ם לְךָ֖ שָׁלֽוֹם׃ (ס) (כז) וְשָׂמ֥וּ אֶת־שְׁמִ֖י עַל־בְּנֵ֣י יִשְׂרָאֵ֑ל וַאֲנִ֖י אֲבָרֲכֵֽם׃ (פ)

(22) The Eternal spoke to Moses: (23) Speak to Aaron and his sons: Thus shall you bless the people of Israel. Say to them: (24) The Eternal bless you and protect you! (25) The Eternal deal kindly and graciously with you! (26) The Eternal bestow favour upon you and grant you peace! (27) Thus they shall link My name with the people of Israel, and I, I will bless them.

According to the Mishnah (Tamid 5:1) the words of the priestly blessings were part of the service during the time of the Second Temple. Some scholars believe that the liturgy of theAmidah (the central portion of the service) developed around the priestly blessing. Rabbinic literature has an additional term for the priestly blessing: nesiyat kappayim "the raising of hands."

There are in fact three separate blessings, which progress from

the blessing of physical protection, through the blessing of spiritual shelter, to the blessing of shalom – wholeness, completion or peace.

Accordingly, the three sections of the priestly benedictions illustrate an ascending order, starting with a blessing concerned with man’s material needs and then dealing with his spiritual wants, and finally reaching a climax combining both these factors together, crowning them with the blessing of peace. This ascending order and increasing surge of blessing is reflected in the language and rhythm. Studies in Bemidbar, Nehama Leibowitz, p. 67

Part of the blessing’spower lies in the simplicity of its structure, which Bible scholar Jacob Milgrom describes as “a rising crescendo”: There are three words in the first line, five in the second, and seven in the third; fifteen consonants in the first line,twenty in the second, and twenty five in the third.The sense conveyed is of increasing,overflowing divine blessing.

The verses that surround the priestly blessing (vv. 22, 27) raise important questions: Why does God dictate to the priests the exact formula they are to use in blessing the people? And why does God emphasize after dictating the words that "I myself will bless them"? The answer to both questions is the same: The Torah wants to underscore the fact that the priests are not the source of blessing. They are, rather, its conduits. "The blessing issues solely from [God]; the priests' function is to channel it." (Rabbi Shai Held)

The opening verse tells the priests to say (א-מ-ר) the blessing, but the closing verse refers to putting (ש-ו-מ) the blessing upon the Israelites. Why?

It is customary for the people to refrain from looking at the kohanim (and vice versa) while reciting this blessing. The kohanim are accustomed to covering their faces and hands with a tallit during the blessing; many members of the congregation are accustomed to doing likewise, casting their eyes downwards and covering their own faces and those of their children with their tallit. In some cases, they may even turn their backs to the kohanim so as to avoid inadvertently seeing them (although the kohanim and the congregation must face one another during the blessing), expressing the feeling that there is a certain “danger” involved in seeing the kohanim during the blessing.

“Resh Lakish said: Whoever gazes at three things, his eyes grow dim: At the rainbow, and at the Nasi (i.e., the leader of Israel), and at the kohanim … [This refers to one] who looks at the kohanim at the time that the Temple was standing, when they stood upon the dukhan and blessed Israel with the Ineffable Name.” (BT Chagiga 16a)

Midrash Tanhuma understands the hand-raising ritual as evoking the relationship between God and Israel. Song of Songs relates how one lover glimpses another: "There he stands behind our wall, gazing through the window, peering through the lattice" (Song 2:9). In the midrashic interpretation, God is the lover peering at Israel through the lattice formed by the hands raised in the priestly blessing.

All this is imaginatively derived from the words of the blessing. The instructions in Naso read Adonai spoke to Moses: Speak to Aaron and his sons: Thus shall you bless the people of Israel (Numbers 6:23). Yet, after the words of the blessing God says: Thus they shall link My name with the people of Israel, and I will bless them. (Numbers 6:27) Which is it? Are the priests blessing the people or is God doing the blessing?

In Midrash Tanhuma the people of Israel question the role of the priests in the blessing, saying to God: "We only need Your blessing." God responds, "I will stand with the priests and bless you." Israel’s request is one we can all relate to: We want the Divine experience; why do we need a go-between? While the image of God as the lover peering through the window is beautiful, it is also quite clear that God is out of reach.

Implicit in all this is that the direct experience of God is better than the mediated one. Implicit as well is that there is a mehitzah, a "barrier", between us and God. At the risk of stating the obvious, this is the only way it can be. In Judaism the human and the Divine are separate and will always be so. Contact with the Divine can be dangerous. Most of the book of Leviticus deals with boundaries that need to be maintained. Yet we strive for that contact, that unmediated spiritual experience. (Rabbi Michal Shekel)

The Shekhinah is said to rest upon the hands of the priests during the blessing and so the custom not to look arose.

This in fact reflects an important theological point: namely, that the priests are not able to give blessing of their own accord. Rather, they serve as intermediaries, vessels of the Divine spirit, delivered by means of their reciting these words. At the time of blessing their own individual personality is, so to speak, obscured by their priestly function. Hence they hide their faces. The lesson taught is ultimately one of humility.

In Israel this blessing is recited daily at shacharit (and at mussaf on shabbatot and yom tov) in the synagogue in the Repetition of the Amidah, during which the kohanim, members of the hereditary priesthood, lift their hands over the congregation and recite this text, word by word. It is not recited in the afternoon, because kohanim must be sober, and so it is not said during those times of day when the kohen might have drunk wine; for that same reason, it is recited at Minhah on fast days, and on Yom Kippur is even recited at Neilah

In Ashkenazi Diaspora it is done at mussaf of festival days.

The formulation of the mitzvah of Birkat Cohanim shows it is a mitzva De'oraita - a positive mitzvah from the Torah for the Cohanim to bless the Jewish People every day. This is how it is codified by the Sefer HaHinuch. So how did the custom of not doing Birkat Cohanim daily start in the Diaspora?
reasons given include:

The custom was to immerse in a mikveh before doing Birkat Cohanim. This was very hard to do in the Winter in Eastern Europe so they stopped doing it every day.

Isserles wrote that "It has become the practice that the Cohanim do not raise their hands in blessing except on Yom Tov, as then they are in a state of happiness because of Yom Tov and a person who is in good spirits should administer the blessing. They are not in a state of happiness on other days even on Shabbatot as they are preoccupied with thoughts concerning their sustenance and over the cessation of their work. Even on Yom Tov they only do it at Musaf as then they are about to leave synagogue and rejoice in the celebration of Yom Tov."

Sephardi communities in diaspora also vary about when they do it - only days torah is read/ only shabbat/ every day/ only yom tov.....

For the past several hundred years this blessing has been recited by parents at the beginning of Shabbat as a way of invoking God's blessing upon their children.

R. Naftali Zvi Yehudah Berlin (Netziv, 1816-1893) picks up on the fact that the blessing, recited over the whole people, is nevertheless stated in the second-person singular, and interprets that each person be granted blessings appropriate to them. "For the one engaged in Torah-blessings for their study; for the one engaged in trade-success in business," and so on. We can take the Netziv's point one significant step further: Divine blessing is not generic but specific to each individual and her needs, dreams, and yearnings. God sees and cherishes us as individuals,and we pray for blessings accordingly.

The Netziv's explanation of "and protect you" goes further:. "May God protect you, lest the very blessing you receive turn into a stumbling block." The blessing of wealth, for example, can lead to greed, or stinginess, or lack of empathy. Or it can lead to a perpetual state of anxiety that one does not have enough or that one may lose what one has earned Crucially, the Netziv points out, even the blessing of Torah learning can yield rotten fruit: The Torah scholar can easily become arrogant or cause a desecration of God's name.

ברוך אתה יי אלהינו מלך העולם אשר קדשנו בקדושתו של אהרון וצונו לברך את עמו ישראל באהבה

The blessing traditionally recited by the priests before blessing the people is highly unusual. They say, "Blessed are You, Eternal our God, Ruler of the universe, who has sanctified us with the sanctity of Aaron and commanded us to bless Your people Israel with love."

Two important questions emerge from this formula: First, why do the priests talk about being sanctified with the sanctity of Aaron instead of employing the usual formula, "who has sanctified us with God's commandments"? And second, why the mention of love at the end of the blessing? This is the only blessing before the performance of a mitzvah in which love is explicitly mentioned (and required).

The answer to our two questions is identical: Blessing depends on love. The Torah does not assign the priests the task of rote recitation. On the contrary, it calls upon them to love the people. Indeed, the Zohar declares that "a priest who does not love the people or is not loved by the people should not raise his hands to bless them" (Naso, 147b). Aaron, the first priest, is remembered as "a lover of peace and a pursuer of peace, one who love[d] people and brought them closer to Torah" (Mishnah, Avot 1:12). "The holiness of Aaron," says R. Shalom Noah Berezovsky (1911-2000), "flowed from his love." [10] A priest devoid of love is a priest in name only.

An archaeological find in Ketef Hinnom (South Jerusalem) by Gabriel Barkay in 1979 demonstrates the antiquity of this blessing at least as far back as the 7th century BCE. 2tiny silver scrolls with different versions of this blessing were discovered, including the phrases “May YHWH bless you and guard you; may YHWH make his face shine upon you.”

They had been worn as amulets by ancient Israelites more than 2600 years ago. Not only does this archaeological discovery tell us that the benediction was in use at a time before we have any hard evidence for the existence of a written Torah; it also tells us something about how the ancients understood and used it as a form of protection.

There is an element of magic here - similar to the superstition around the mezuzah scroll. There is also potentially a connection to tefillin.

The Reform/Conservative/Liberal Movements no longer classify cohanim is a separate category, on the twofold basis that we no longer connect with God through Temple ritual and no longer pray for its rebuilding, nor for the return of the sacrifices) and because we cannot any longer be sure that those who believe themselves to be cohanim really are of that priestly descent nor that there has not been a dislocation in their status. Because there are religious laws which disbenefit cohanim we have abolished any meaning in this category in order to free the people to marry whom they will etc.

The Birkat Cohanim/Nesiyat Cappayim is therefore not given in our liturgy in the way that the orthodox world does it. However the words of the prayer are powerful and meaningful, so this blessing is often given by the service leader at the end of the service, and in other liturgical contexts.