Throughout the year the silent Amida is meant to be just that, silent, but the Shulhan Aruch (Orah Haim 582:9) explains that on Rosh Hashana and Yom Kippur it is customary for individuals to pray out loud. The Shulhan Aruch adds that there is no concern that this will be a distraction since Siddurim are commonplace. Despite this ruling this practice is rare, and the HIDA (Mahzik Beracha), Rabbi Haim Palagi and others say that according Kabbala, one should not raise one’s voice on the Yamim Noraim when there is increased Divine judgment. The HIDA adds that lay people would be permitted to pray out loud as this is the letter of the law, but for those who are learned in Kabbala, it should be avoided.
The Moroccan community has a custom in which an assistant Hazan recites the Amida of Rosh Hashana and Yom Kippur out loud while the congregation is praying silently [listen to audio for an example]. This was originally done to facilitate the prayer for those who were not accustomed to praying or for those who were illiterate, and because Siddurim were not as abundant as today. Another advantage of this practice is that it sets the pace so that the congregants can be aware of when the Shofar will be blasted during the silent Musaf Amida. Since most people are proficient in prayer nowadays, there are Moroccan communities that have dropped this custom.
Summary: The custom among some Moroccan communities is that an assistant Hazan recites the silent Amida out loud on Rosh Hashana and Yom Kippur.