What is kaddish?

It is a memorial prayer. It's an affirmation of life and goodness and God. It likely became associated with mourning because of the tradition of shiva, of going to the house of the mourner and doing prayers and study together. There's a kaddish prayer that you do at the end of study, so over time, it probably became associated with the mourner. The mourner says the prayer every day of the first year and then once a year, on the Yahrzeit, the anniversary of the death. It's the prayer that ends every service in the Jewish tradition.