Eli Y,
“Now let me ask the non-Chabad folks a question if I may: What does one achieve by saying Kaddish?”
Kaddish is a public sanctification of Hashem, and by saying it, one prompts a minyan of Jews to publicly sanctify Hashem in response (y’hei sh’mei raba…). This is an extremely holy and meritorious act. To do so in the context of mourning is extremely powerful, because the mourner declares the greatness of Hashem even through his pain. Since this tremendous mitzva was done for the sake of the deceased, the merits are also added to the merits of the deceased.