There is an abundance of mystical significance to the Kaddish prayer, which this article will touch upon; but first, some basics…
The most immediately noteworthy thing about Kaddish is that even though it is chanted by mourners, it is not a prayer for the dead. Exactly the opposite. As you can glean from just a superficial reading, it consists solely of lofty praises for the Creator and heartfelt imploring for the perfection of Creation.
There are four variations of Kaddish: 'Whole,' 'Half,' 'Rabbis',' and 'Orphans'. The first two are said only by the prayer leader, the latter two by the mourners in unison, even though anyone who participates in the study of the Oral Torah is entitled to say the Rabbi's Kaddish.
The obligation of reciting Kaddish is part of the mourning observances for a parent, sibling, offspring or spouse for one month, starting immediately upon burial. For parents, the mourning continues through the rest of the year because of the obligation of 'honor' in addition to the mourning. When possible, it is preferable for a son of the deceased to be the Kaddish-sayer, rather than any other relative.
… Rabbi Akiva's mystical encounter with an lifelong sinner who had died…
So if Kaddish makes no mention of the dead, and if it is so special, why do mourners say it? For one thing, it is an honor for the soul of the deceased that its 'representative' is saying the Kaddish. Primarily, it is a great merit and help for the soul during its year of judgment after death. This is especially true when it is said by the son(s) of the deceased, and especially when those sons lead observant Jewish lives.
One way we know of the extraordinary redemptive power of Kaddish is from a dramatic story that begins with Rabbi Akiva's mystical encounter with an lifelong sinner who had died and was suffering grievous, unrelenting punishment. The sinner informed the rabbi that only if his sole surviving child would recite the Borchu and Kaddish could he be redeemed. With great effort, Rabbi Akiva located the lad and taught him these prayers. When the youngster finally recited Kaddish in the synagogue, he earned his father's release.
Saying Kaddish can also be very helpful for the mourners themselves. Just thinking about the ideas expressed as you say them (or before, or after) helps bring acceptance of the tragic loss, even when it is seemingly unreasonable and still painful. It is important to remember that G‑d has a master plan.
Having to chant Kaddish in public (a minyan is required) and, often, simultaneously with others, also helps to move the mourner beyond personal woes and to start thinking more communally. Kaddish-saying stops at eleven months, because "the judgment of the righteous concludes after 11 months, the wicked after 12," so to continue into the twelfth month would be to cast aspersion on the departed.
The four letters of the word Mishna(h) can be re-arranged to spell Neshama(h), meaning 'soul'…
In some communities, the mourner teaches out loud a bit of Mishna and adds another Rabbis' Kaddish at the end of each of the three daily services. The recommended texts, included in many versions of the siddur, are very special, each citing various cases where the conclusion is 'Pure.'
The four letters of the word Mishna(h) can be re-arranged to spell Neshama(h), meaning "soul" in Hebrew, which explains why Mishna is the preferred vehicle of study in this situation.
Kaddish is not said in Hebrew. Rather, it is recited in Aramaic, the main spoken language of the Jewish people from the period of the destruction of the first Temple (around 2400 years ago) past the completion of the Talmud (around 1400 years ago). If the reason is, as is traditionally understood, that the majority of the people were not fluent in the Holy Tongue, we can see how important it is for the mourner to understand the prayer he is saying.
Deep mysteries are embedded in the letters, words, and phrases of the Aramaic…
According to the Zohar, however, we employ a secular language because subjugating the "External Forces" (or the chitzonim) and utilizing them as a vehicle for holiness enables us to accomplish a profound goal expressed in Kaddish: "Let His Great Name be magnified and sanctified on earth."
Another reason for reciting Kaddish in its original language, Aramaic, is that deep mysteries are embedded in the letters, words, and phrases of the Aramaic. Most of them we cannot fathom easily, but some are relatively accessible.
The Kaddish begins with the four words Yitgadal v'yitkadash shmei rabbah (meaning "Exalted and sanctified be His great Name"). These four words parallel the four letters of G‑d's holiest name. This is one reason we already respond "Amen" after only four words.
The main part of the response to the Kaddish is the line: Amen. Yihai shmai rabbah m'vorach, l'olam u'olmai umayah (meaning "May his great name be blessed forever, eternally"). This phrase contains seven words and 28 letters. The very first verse of the Torah, Bereishit bara Elokim et hashamayim v'et ha'aretz ("In the beginning G‑d created the heaven and the earth"), also contains seven words and 28 letters. In addition, the introductory line to the Ten Commandments (Ex. 20:1), Vayadabair Elokim et kol hadevarim ha'elah, laimor ("And G‑d spoke all these words, saying"), also contains seven words and 28 letters.
This all-important seven-word sentence is followed by seven expressions of praise…
Thus, saying Kaddish includes the privilege of linking to these two monumental events. The seven-word response also affirms our belief that G‑d is the creator of all, and also intimately involved with his creation. This all-important seven-word sentence is followed by seven expressions of praise, beginning with yisbareich (be blessed). There should be no pause between saying almaya and continuing yisbareich, etc., for the wish that His Name be blessed generates immediately the demand that He be forever extolled.
The Talmud and Zohar agree that responding, "Amen. May His great Name be blessed forever and ever," with vigor can nullify an adverse decree of seventy or even one hundred years." Because of this, nearly everyone calls out this response with extra intensity. Remember, it must also be said with total concentration for a decree to be annulled.
When the children lead good Jewish lives, full of mitzvah observance and Torah study, this is even more meritorious for the soul of the parents than saying Kaddish. In fact, the earliest extant records of Kaddish seem to indicate that Orphan's Kaddish was expected to be said by pre-bar mitzvah boys. From adult offspring, more is to be expected. It is even more beneficial, both for the souls above and those still alive in this world, when as a result of the death, offspring, other family members and all those close to the deceased examine their deeds and resolve to improve accordingly. As it is written, "the living should place it upon their hearts."
And when we do, that helps to "bring forth his redemption and hasten the coming of Mashiach." Amen!