The Kaddish is one of the most famous prayers offered during the service. Kaddish is recited only when there is a minyan (quorum of ten). There is a special version of the Kaddish that is recited specifically by mourners called Mourner's Kaddish. It is interesting to note that many Jews have returned to observance of Judaism and synagogue participation through fulfilling the obligation to say Kaddish for a departed loved one.
The Shulchan Aruch (Code of Jewish Law) explains that for a parent Kaddish is recited for 11 months, whereas for a spouse, sibling or child it is recited for 30 days.
The text of Kaddish is in Aramaic, the vernacular of the Jewish people at the time of its composition (Talmudic times).
We find that the saying of Kaddish by a next of kin is a great merit for the soul that has passed away. Why is that so? Can our actions in this physical world affect those who have passed on to the spiritual world? The answer is a resounding yes, and can be better understood by examining the Kaddish itself.
Many find it intriguing that this prayer, the preeminent prayer said for those who have passed on, makes absolutely no mention of death, loss or mourning. Nor is there mention of the person who died. Kaddish speaks of G‑d's greatness. In fact, Kaddish is an affirmation of belief in the Almighty and His unlimited power. If one were to boil down the theme of Kaddish, it would be that G‑d is great and everything comes from G‑d, so everything that occurs is ultimately for the good.
This is a profound statement for one in the midst of grieving. It is precisely this type of statement that benefits the soul of the deceased, and proves that those left behind can maintain an important connection with those who have passed.
Our tradition teaches that following death the soul ascends and is judged according to its deeds while alive in the physical realm. Everything accomplished by the soul, both positive and negative, is carefully considered. One of the greatest legacies one can leave behind is a family that has been inspired to serve G‑d, even during times of distress.
When in the midst of this judgment the hallowed words of Kaddish ascend, uttered by those who grieve most intensely, this serves as a great merit for the soul. Obviously, a person who inspired those around her to such an awesome level of faith and commitment has fulfilled many great deeds and is prepared for the manifested light of the Creator experienced in Heaven.
It is for this same reason that many undertake to do mitzvot in honor and memory of those who have passed away. They are seeking to prove that the departed is truly a worthy soul deserving of a lichtig Gan Eden, a "luminous Paradise."
It turns out the intuitive feelings of many that Kaddish must be recited is exactly right. It may be argued that saying Kaddish is the ultimate sign of love and respect that one can do for those who have passed away.
You write above that someone’s passing is for the good; can you please expand on that assertion? I understand that everything G-d does is for the good, and that our true purpose in this world is to merit and enter Olam Haba, but I find it extremely insensitive to the family of the departed when people (usually rabbis) give speeches at a house of mourning saying that “this was for the good” (I’d make the same observation for other tragedies involving loss of life or limb). It’d be more respectful of the family’s pain and sorrow to instead say that we grieve the loss deeply, while simultaneously recognizing that G-d has His reasons and that we all are allotted a certain number of years on this earth. I don’t think anyone is comforted when told that their loved one’s death was for the good.
It goes without saying that when a person passes away we do not say in the house of mourning that it is all for the good. What we do hear rabbis speak about is the World to Come and how the soul is in a state of peace and comfort. Many people in the house of mourning are concerned about where the soul of their loved one is, and how they are faring, this is actually reassuring them that all is well with the soul of the departed.
But in giving our thanks to G-d we do include in the subjects being covered many that are not good or pleasant to our nature and some of them may even be classified as evil. Personally, I refuse to give thanks for these kinds, but I know that orthodox Jews thank G-d even when something bad or unpleasant happens. So, in a house of mourning apparently it is OK to recite our thanks too!