Stone Edition Chumash
As soon as the Jews entered the Land, they were to assemble at two mountains [Mount Gerizim and Mount Ebal], for a new acceptance of the Torah, There, twelve commandments would be enumerated, and the people would acknowledge publicly that blessing await those who observe and curses will befall those who spurn then. Six tribes would stand on one mountain and six tribes on the other, with the Ark, the Kohanim, and the Levites in the valley between them. The Levites in the valley would loudly pronounce the blessings and curses, and the tribes on the mountops could call out, “Amen!” Thus, the very entry into the Land would include a pledge of allegiance, as it were, to the Torah that constitutes the essence of Jewish nationhood.
Rashi on Deuteronomy 27:12
לברך את העם [THESE SHALL STAND UP …] TO BLESS THE PEOPLE — The procedure was as is found in Treatise Sotah 32a: Six tribes ascended the top of Mount Gerizim and the other six the top of Mount Ebal, the priests, the Levites and the Ark remaining below in the midst (i.e. in the valley between). The Levites turned their faces towards Mount Gerizim and began to recite the blessing: “Blessed be the man that does not make any graven or molten image etc.”, and both these and those (the tribes on Mount Gerizim and those on Mount Ebal) answered “Amen”! Then they turned their faces towards Mount Ebal and began to recite the curse, saying: “Cursed be the man who maketh any graven [or molten image]” — and so in the case of all of them (the curses set forth here) till the last: “Cursed be he that does not uphold [all the words of this law to do them]” (cf. Rashi on Deuteronomy 11:29).
Rashbam on Deuteronomy 27:15
ושם בסתר, there are a total of 12 “curses” corresponding to the 12 tribes, all of the sins mentioned in them being of the type that one commits in private, when one is unobserved and no witnesses are present. I will explain all of them. There are only two of these which are sometimes committed in private and sometimes in public. These are idolatry and striking one’s fellow Jew. This is the reason that the Torah mentions the word בסתר specifically in connection with thee two sins that are listed here. The reason is that for sins committed in public there is no need to utter a curse as people sinning in public are not frightened of the curses either. Not only that, the court has a chance to deal with crimes/sins committed in public.
Rabbeynu Bachya on Deuteronomy 27:15
The reason the Torah singled out these eleven sins from among all the others, is that they result in exile for the people if they become habitually guilty of these sins. Now that the people were about to enter the Holy Land, it was important for them to realise which sins, if committed knowingly, would result in their forfeiting the land.
According to the plain meaning of the text, the selection of these eleven sins was due to their being capable of being perpetrated without the sinner having to expose himself publicly and therefore facing either the court or the disapproval of his peers. The Torah started by listing the worst of these sins, a sin committed vis-a-vis one’s Creator only. It followed with sins which are perpetrated between man and his parents, not necessarily involving anyone else. Who would know if the son belittled his parents? Similarly, the sin of השגת גבול, making adjustments (illegal) to he boundary between one’s property and that of one’s neighbour, is one committed surreptitiously, not publicly. Misleading a blind person by causing him to go astray is also something which the person against whom the sin has been committed is unable to pinpoint and accuse the sinner of. Perverting the judgment of proselytes, orphans, or widows also belongs into this category as these people have no one who will take up their cause; the sinner expects to get away with what he does. Perverting justice is altogether something that is covered up by the one doing it. The various examples of illicit sexual relations are in the nature of something secretive seeing they are perpetrated between consenting adults, neither of which is liable to admit to having been involved in such acts. Moreover, the examples of which the Torah speaks here are the kind that no one would be suspected of in the first place, thus preserving the likelihood that it will go undetected except by G’d.
Or HaChayim on Deuteronomy 27:15
and the entire people are to respond by saying "Amen." In this instance the Torah was not satisfied to write ואמר כל העם as it did with respect to all the other ten curses listed here. The Torah wanted to make certain that the Israelites were required to respond (not merely say). Had the Torah not written the word וענו at this point we might have thought that it was the Levites who had to say the words ואמר כל העם, "and the entire people are to say."
Shavuot 36a
§ Rabbi Yosei, son of Rabbi Ḥanina, says with regard to the term amen: There is an element of oath within it, there is an element of acceptance of the statement and agreement within it, and there is an element of confirmation of the statement, i.e., that he believes and prays that the statement will be fulfilled, within it. The Gemara elaborates: There is an element of oath within it, as it is written: “And the priest shall administer an oath to the woman…and the woman shall say: Amen, amen” (Numbers 5:21–22). “Amen” is the oath that the woman takes. There is an element of acceptance of the statement within it, as it is written: “Cursed is he who shall not confirm the matters of this Torah to perform them; and all the people shall say: Amen” (Deuteronomy 27:26), expressing their agreement to fulfill all the matters of the Torah. There is an element of confirmation of the statement within it, as it is written: “And Jeremiah the prophet said: Amen, may the Lord do so; may the Lord uphold your statement” (Jeremiah 28:6).
Shulchan Aruch, Or Haayim 215:2
If a Jew hears someone say part of a bracha, even if he didn't hear the entire bracha from the beginning to the end and he is not bound by that bracha, [but] he still has to say ‘Amen.’” Even further, the Polish talmudist Moshe Ben Yisrael Isserles says that ‘You can even say Amen after a Gentile makes a blessing!’”
Dr. Samuel Lebens, chair of the Association for the Philosophy of Judaism at University of London, wrote in The Power of 'Amen' on Yom Kippur:
“The vast majority of Jews will be marking Yom Kippur in one way or another. And for many of us, the experience of staring blankly upon a prayer book written in an ancient and unfamiliar language is daunting. But if you can say nothing else, you can still say "Amen” and you can know, that in doing so, you have really said it all – (1) you have committed yourself, with that one word, to becoming a better Jew, (2) you have accepted upon yourself the consequences of your identity, and (3) you have expressed the prayer that you will live up to your potential and receive abundant blessings in return.
Don’t look over at those Jews who know what they’re doing with the prayer book, as they fervently follow each word of the service, beating away at their chests as they read the confession; don’t let your head hang in shame that you can’t muster the appropriate feelings, nor concentrate through a cumbersome liturgy. Know that, in the words of the Midrash, "Before the Holy One, blessed be He, there is nothing greater than a Jew who says ‘amen’ ...." That single word, uttered with sincerity, can make the whole day worthwhile.”