Soul Services: Saying Kaddish
There is an abundance of mystical significance to 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 dead. Exactly opposite. As you can glean from just a superficial reading, it consists solely of lofty praises for Creator and heartfelt imploring for perfection of Creation.
There are four variations of Kaddish: 'Whole,' 'Half,' 'Rabbis',' and 'Orphans'.' The first two are said only by prayer leader, latter two by mourners in unison, even though anyone who participates in study of Oral Torah is entitled to say Rabbi's Kaddish.
The obligation of reciting Kaddish is part of mourning observances for a parent, sibling, offspring or spouse for one month, starting immediately upon burial. For parents, mourning continues through rest of year because of obligation of 'honor' in addition to mourning. When possible, it is preferable for a son of deceased to be 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 dead, and if it is so special, why do mourners say it? For one thing, it is an honor for soul of deceased that its 'representative' is saying Kaddish. Primarily, it is a great merit and help for soul during its year of judgment after death. This is especially true when it is said by son(s) of deceased, and especially when those sons lead observant Jewish lives.
One way we know of 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 rabbi that only if his sole surviving child would recite Borchu and Kaddish could he be redeemed. With great effort, Rabbi Akiva located lad and taught him these prayers. When youngster finally recited Kaddish in synagogue, he earned his father's release. 
Saying Kaddish can also be very helpful for mourners themselves. Just thinking about ideas expressed as you say them (or before, or after) helps bring acceptance of 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 mourner beyond personal woes and to start thinking more communally. Kaddish-saying stops at eleven months, because "the judgment of righteous concludes after 11 months, wicked after 12," so to continue into twelfth month would be to cast aspersion on departed.
" The four letters of word Mishna(h) can be re-arranged to spell Neshama(h), meaning 'soul'..." In some communities, mourner teaches out loud a bit of Mishna and adds another Rabbis' Kaddish at end of each of three daily services. The recommended texts, included in many versions of siddur, are very special, each citing various cases where conclusion is 'Pure.'
Mishna is preferred vehicle of study in this situation.
Kaddish is not said in Hebrew. Rather, it is recited in Aramaic, main spoken language of Jewish people from period of destruction of first Temple (around 2400 years ago) past completion of Talmud (around 1400 years ago). If reason is, as is traditionally understood, that majority of people were not fluent in Holy Tongue, we can see how important it is for mourner to understand prayer he is saying.