Yom Kippur, the holiest day in the Jewish calendar, is a day of repentance and forgiveness, which this scene in the film tries to depict. Some would find it mawkish and overly sentimental; others hitting just the right note. I guess it would depend on how you view such things.
As for Kol Nidre (English: "All vows"), it is an Aramaic prayer dating to the Genoic Period of Judaism, making the prayer 1,000 years old. This is a particularly solemn occasion in the synagogue service in what is a very solemn day. In the Jewish Encyclopedia, we learn:
Form of Prayer.Before sunset on the eve of the Day of Atonement, when the congregation has gathered in the synagogue, the Ark is opened and two rabbis, or two leading men in the community, take from it two Torah-scrolls. Then they take their places, one on each side of the ḥazzan, and the three recite in concert a formula beginning with the words, which runs as follows:In the tribunal of heaven and the tribunal of earth, by the permission of God—blessed be He—and by the permission of this holy congregation, we hold it lawful to pray with the transgressors.Thereupon the cantor chants the Aramaic prayer beginning with the words "Kol Nidre," with its marvelously plaintive and touching melody, and, gradually increasing in volume from pianissimo to fortissimo, repeats three times the following words:All vows, obligations, oaths, and anathemas, whether called 'ḳonam,' 'ḳonas,' or by any other name, which we may vow, or swear, or pledge, or whereby we may be bound, from this Day of Atonement until the next (whose happy coming we await), we do repent. May they be deemed absolved, forgiven, annulled, and void, and made of no effect; they shall not bind us nor have power over us. The vows shall not be reckoned vows; the obligations shall not be obligatory; nor the oaths be oaths.The leader and the congregation then say together:(Num. xv. 26).This also is repeated three times. The ḥazzan then closes with the benediction, "Blessed art thou, O Lord our God, King of the Universe, who hast preserved us and hast brought us to enjoy this season." In many congregations Num. xiv. 19-20 is recited before this benediction. After it the Torah-scrolls are replaced, and the customary evening service begins.And it shall be forgiven all the congregation of the children of Israel, and the stranger that sojourneth among them, seeing all the people were in ignorance.