Use in The Synagogue
Aleinu is recited with all the congregants standing. One reason for this is noble sentiments are expressed, but also that the first and last letters of the prayer spell עד - "witness" - and it is appropriate for a witness to stand when testifying.
The original context of this prayer was as part of the middle paragraphs of the Amidah prayer in the mussaf (additional) service on Rosh Hashanah (Jewish New Year), and more specifically in the passage known as Malchuyot (the kingdom of God). In this context it includes both paragraphs of the prayer. The first paragraph is also included at the equivalent point in the liturgy for Yom Kippur.
In the Middle Ages the custom grew up of reciting the first paragraph every day, at the end either of the morning service alone or of all the prayer services for the day. In the 16th century the kabbalist Hayim Vital, recording the opinions of Isaac Luria, ruled that both paragraphs should be included in all services, and should end with the verse "on that day the Lord shall be one and His Name one". This has been accepted in almost all communities except for the Spanish and Portuguese Jews, who retain the "short Alenu". The custom according to some North African prayer books is to recite the second paragraph only at the conclusion of weekday morning services.
In the daily and Sabbath services, when the line (numbered, above, as line 9, here translated literally) "But we bend our knees and bow" is recited, the worshipper will flex his knees and then bend from the waist, straightening up by the time the words "before (lif'nei) the King of kings of kings" are reached. But on the High Holy Days of Rosh Hashana and Yom Kippur, the worshipper will not merely flex and bend, but will actually get down on his knees at those words, and some Sefardic and Mizrahi congregants will prostrate themselves on the floor (in those synagogues with sufficient floor space).
In Orthodox and Conservative congregations, the Torah Ark remains closed while it is recited (except on Rosh Hashana and Yom Kippur, when the Ark is opened), but in Reform congregations the Ark is opened whenever Aleinu is recited. In Sefardic congregations, as well as in the Askenazic traditions of Frankfurt and Mainz, Aleinu is not followed by the Mourner's Kaddish (because, variously, Aleinu was whispered to avoid antagonizing the Christian authorities, or because Aleinu is not a reading from Scripture), elsewhere it is.
Read more about this topic: Aleinu