Tikkun means repair, but also arrangement, setting in order, completion. In Etz Chaim, a whole gate is called Shaar HaTikkun, the gate of repair, and it opens this way: "when it arose in the will of the Emanator to revive the dead and to repair those broken and fallen kings." The "dead" are the broken vessels of the previous entry. Tikkun therefore begins above, by an act of the Creator: the lights and the vessels are reorganized no longer as isolated points, but as complete figures, partzufim, in which each Sefirah contains the ten and all are linked. It is this new solidity that allows the light to be carried without breaking.
But tikkun is not completed above. Shaar HaKlalim says it with rare clarity: even after the good was sifted from the waste, "the sparks of holiness remained inside." And it adds: "this is what is left for us to repair, through prayer and good deeds." Every mitzvah performed, every prayer said with the heart, takes part in lifting these sparks held captive in the husks. The text adds that the souls of the righteous, when they leave this world, raise them from one world to the next, from Action to Formation, from Formation to Creation, then to Emanation, "and bring the great light back to its place."
You see what this changes. The story that began with the Infinite ends in your hands. The tzimtzum, the kav, the breaking, none of it was told to impress you, but to tell you where you are: in a world full of sparks that wait, and with the power to lift them. Etz Chaim counts two hundred and eighty-eight sparks left in the broken vessels "to revive them at the time of the repair." The repair was thus planned from the fall itself.
Daily prayer recalls it without naming it. The Alenu, which closes every service, asks "to repair the world under the kingship of the Almighty," letaken olam bemalkhut Shaddai. In the Alenu, these words aim at the removal of idolatry under the kingship of G-d; this phrase, older than the Kabbalah of Safed, was reread by it in the sense of tikkun.
A last point, to avoid a misreading. Tikkun is not first of all a social program or a reform of the outer world: it is the repair of the relationship between the world and its Creator, which goes through precise, humble, often invisible acts. Cordovero's Tomer Devorah begins exactly there: a person must resemble the Creator in deeds, not only in form. That is tikkun at human height, and it is the subject of the whole next section.