When recited in the synagogue, both shaharit and minha (the morning and afternoon prayer services) include the Amida prayer, first recited by each individual congregant, and then followed by an out-loud repetition by the ḥazzan. This tradition has its source in the last Mishna in Massekhet Rosh HaShana (33b) where the Mishna teaches that both the individual and the ḥazzan are obligated to recite the prayer. Rabban Gamliel argues that the community can listen to the recitation of the ḥazzan, who represents the community (his title, in fact, is shaliah zibbur – the congregation’s messenger), and fulfill their obligation without reciting it themselves.
According to the Shulhan Arukh (Orah Hayyim 124:1), a person who is not familiar with the prayers can listen to the ḥazzan and fulfill his obligation on the condition that he remain silent throughout the repetition and pay close attention to every word recited from beginning to end. Such a person should treat this as he would his own Amida – he should take three steps back at the end, etc. The Shulhan Arukh HaRav rules that it is essential that he understand at least the first berakha; otherwise he would be better off saying the Amida in a language that he understands.
This is all true for someone who is not expert enough to pray on his own. If someone is a baki – an expert in the prayers – it is not clear whether we follow Rabban Gamliel’s ruling. The Magen Avraham, for example, rules that a baki cannot fulfill his obligation in prayer by simply listening to the repetition of the ḥazzan.
Although there are arguments as to whether we accept Rabban Gamilel’s position all year round, the clear conclusion of the Gemara is that on Rosh HaShana we follow his opinion mishum de-avshi berakhot – because the extra blessings in the Rosh HaShana prayers are long and unfamiliar. The Rosh suggests that the expression, “mishum de-avshi berakhot” refers to the noise in the synagogue during Rosh HaShana prayers. Unlike regular days, when most people are familiar with the prayers and say them quietly, on Rosh HaShana people are more likely to say them aloud, making it difficult to concentrate. Thus, on Rosh HaShana everyone can fulfill the obligation of tefillah by listening to the ḥazzan.