The Rosh explains that there is nothing special about Rosh HaShana in this regard; this declaration can be made any day of the year. The Gemara mentions Rosh HaShana simply as a specific day on which this could be done with intent for the upcoming year. Many argue that this Gemara is the source for the tradition of saying the Kol Nidrei prayer – in which we request that all of our vows be annulled – at the beginning of Yom Kippur. The fact that we say it on Yom Kippur rather than Rosh HaShana is not of great significance, given that we have already established that Rosh HaShana was suggested by the Gemara simply as an example. Therefore, Yom Kippur, when all Jews traditionally come to the synagogue, is the most appropriate day to recite this publicly. Furthermore, a day set aside for atonement and forgiveness would seem to be a good day for such a prayer, particularly in light of the fact that Yom Kippur is referred to by the prophet Yehezkel as Rosh HaShana (see Yehezkel 40:1).
The efficacy of this tradition is discussed by the various commentaries. The Ge’onim generally reject the idea of a blanket hatarat nedarim (annulment of vows) and did not practice this in their communities. Rav Hai Ga’on suggests that rather than a request for annulment, the congregation should recite the prayer as a request for forgiveness for all those who transgressed vows they had taken. Nevertheless, many follow the position of Rabbeinu Tam, who accepts the ruling of the Gemara as stated and permits a person to make a condition that all vows made during the upcoming year should be declared void. The declaration is made in a public forum in order to make the matter known to all.