The Kaddish is a prayer that praises God and expresses a yearning for the establishment of God's kingdom on earth. The emotional reactions inspired by the Kaddish come from the circumstances in which it is said: it is recited at funerals and by mourners, and sons are required to say Kaddish for eleven months after the death of a parent.
The word Kaddish means sanctification, and the prayer is a sanctification of God's name. Kaddish is only said with a minyan (prayer quorum of ten men), following a psalm or prayer that has been said in the presence of a minyan, since the essence of the Kaddish is public sanctification. The one who says Kaddish always stands. Whether other worshippers sit or stand depends on the congregation. It is customary for all the mourners in the congregation to recite Kaddish in unison. A child under the age of thirteen may say the Mourner's Kaddish if he has lost one of his parents. Most religious authorities allow a daughter to say Kaddish, although she is under no religious obligation to do so. The Mourner's Kaddish is recited for eleven months from the day of the death and also on the yahrzeit (anniversary of a death). A person may say Kaddish not only for parents, but also for a child, brother, or in-law. An adopted son should say it for adoptive parents who raised him. The Rabbinical Kaddish, Half Kaddish, and Whole Kaddish may be said by a chazzan (cantor - prayer leader) who is not a mourner and has both parents living.
The first mention of mourners saying Kaddish at the end of the service is in a thirteenth century halakhic writing called the Or Zarua. The Kaddish at the end of the service became designated as Kaddish Yatom or Mourner's Kaddish (literally, "Orphan's Kaddish"). It is customary for Kaddish Yatom to also be said before Psukei d'Zimra of shacharit. Although Kaddish contains no reference to death, it has become the prayer for mourners to say. One explanation is that it is an expression of acceptance of Divine judgment and righteousness at a time when a person may easily become bitter and reject God. Another explanation is that by sanctifying God's name in public, the mourners increase the merit of the deceased person. Kaddish is a way in which children can continue to show respect and concern for their parents even after they have died.
The opening words, yitgadal t'yitkadash, were inspired by Ezekiel 38:23 when the prophet envisions a time when God will become great in the eyes of all the nations. The response of the listeners to the first lines of the mourners is a public declaration of the belief that God is great and holy: Yehei Shmei rabba mevorakh l'olam ul'almei almaya (May His great Name be blessed forever and ever). This response is central to the Kaddish and should be said out loud.
The earliest version of Kaddish dates back to the time of the Second Temple. This Kaddish is called the "Half Kaddish." Over time, the custom developed for the chazzan to say the Half Kaddish following Pesukei d'Zimra of the morning service, after the Amidah or the Tahanun and after Torah reading. He also says it before the Amidah at mincha, maariv, and musaf.
Kaddish was not originally said by mourners, but rather by the rabbis when they finished giving sermons on Sabbath afternoons and later, when they finished studying a section of midrash or aggada. This practice developed in Babylonia where most people understood only Aramaic and sermons were given in Aramaic so Kaddish was said in the vernacular. This is why it is currently said in Aramaic. This "Rabbinical Kaddish" (Kaddish d'Rabbanan) is still said after studying midrash or aggada or after reading them as part of the service. It differs from the regular Kaddish because of its inclusion of a prayer for rabbis, scholars and their disciples. While anyone may say this Kaddish, it has become the custom for mourners to say the Rabbinical Kaddish in addition to the Mourner's Kaddish.
By Talmudic times, it became customary to conclude the prayer service with the Kaddish. A sentence was added (the line beginning titkabel, "let be accepted") that replaces the passage for the rabbis and disciples and asks God to accept all prayers that were recited. This Kaddish is called Kaddish Shalem (Whole or Full Kaddish) and is still said by the chazzan at the end of the service. The full Kaddish includes two sentences, added to the Half Kaddish around the eighth century, that reflect the traditional yearning for peace (Yehei shlomo rabba and Oseh shalom).
A last form of the Kaddish, known as "The Great Kaddish" is said at a siyum, when a tractate of the Talmud is completed. The first passage of this Kaddish contains a prayer for the rebuilding of Jerusalem and the Temple and refers to a world-to-come where the dead will be raised to eternal life. This Kaddish is also said at a graveside at a time of burial, although it is not recited if the burial takes place on a day in which Tahanun is omitted from the daily service.