A mourner says Kaddish to help along the soul of the deceased in its journey upwards.
We may look as though we are each traveling our own road, but according to Jewish tradition, we are very tied to one another. Children, especially, are.
Rabbi Isaac Luria, the Ari, the greatest of the Kabbalists, described the family tree as a great river. Parents are upstream, children downstream. Whatever occurs upstream must flow downstream. And so, children inherit the unresolved baggage of their parents.
If so, the Ari tells us, it must be that children are empowered to repair their parents' arm of the river. Otherwise, the world would be stuck in a no-win situation—you receive all the problems from upstream without any recourse to repair them at their source.
And so every child is empowered to carry his parents higher than the parents can carry themselves. As the sages of the Talmud described the situation, "A parent can bring a child into this world, but a child can bring a parent into the world to come."
A parent cannot guarantee a child a place in the world to come. A child, however, can bring the soul of his parents into their proper resting place after they have left this world.
How does the child do that? As the parent's soul leaves this world, everything about that soul is taken into account. What's most important, however, is what this soul has left behind. When a child of that parent is doing whatever he or she can to bring more light and holiness into this world, the soul is able to climb higher, despite whatever heavy baggage may be holding it back.
The Kaddish, as we explained above, is one of those ways to draw in that light and make it shine bright. There are, of course, other ways as well: Charity, Torah Study, raising another generation of good Jews…
Even if there is no son who can say the Kaddish, another Jewish male is still able to help the soul along by saying the Kaddish and by dedicating charity in honor of the deceased. After all, we are all connected. In truth, the Ari taught, we are all only one soul in many different bodies.