Although physical human bodies die, human souls never die. The Catechism of the Catholic Church teaches that every spiritual soul "is immortal: It does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection" (CCC 366).
So at the moment of death, the soul separates from the body, is judged immediately, and enters either heaven (immediately or through purgatory) or hell.
Each man receives his eternal retribution in his immortal soul at the very moment of his death, in a particular judgment that refers his life to Christ: either entrance into the blessedness of heaven—through a purification or immediately—or immediate and everlasting damnation. (CCC 1022)
(For scriptural evidence of this, see Luke 16:22; 23:43; 2 Cor. 5:8; Phil. 1:23.)
Every soul will unite with its resurrected body just prior to the Last Judgment ("Judgment Day") when Christ returns:
In the presence of Christ, who is Truth itself, the truth of each man’s relationship with God will be laid bare. The Last Judgment will reveal even to its furthest consequences the good each person has done or failed to do during his earthly life . . .
The Last Judgment will come when Christ returns in glory. Only the Father knows the day and the hour; only he determines the moment of its coming. Then through his Son Jesus Christ he will pronounce the final word on all history. We shall know the ultimate meaning of the whole work of creation and of the entire economy of salvation and understand the marvelous ways by which his Providence led everything towards its final end. The Last Judgment will reveal that God’s justice triumphs over all the injustices committed by his creatures and that God’s love is stronger than death. (CCC 1039-1040)