The divine indwelling is the Trinity present in the soul of a just person. In 1 Corinthians 3:16, St. Paul asks, "Do you not know that you are the temple of God and that the Spirit of God dwells in you?"
The Catechism of the Catholic Church in paragraphs 1265 teaches, "Baptism ... makes" a person "a temple of the Holy Spirit." The Holy Spirit is emphasized because He is sent by God the Father, as St. Paul in Galatians 4:6 writes: "God has sent the Spirit of his Son into our hearts, crying, 'Abba, Father.'" In John 14:16–17, Christ says, "I will ask the Father and he will give you another Advocate to dwell with you forever, the Spirit of truth. ... [Y]ou shall know him, because he will dwell with you and be in you."
The Holy Trinity cannot be separated, as the Son is eternally proceeding from the Father, and the Holy Spirit is eternally proceeding from the Father and the Son, meaning there was never a time when this was not the case. Divine activity outside of the Trinity Itself, for instance, sanctifying a soul, is said to be accomplished by all three Divine Persons acting in unison as the One God.
The presence of God in a person's soul is what causes sanctifying grace, much like electricity in a light bulb causes light. It is all three Persons acting collectively Who produce sanctifying grace in a soul, as St. Thomas Aquinas teaches: "[T]he effect of grace is also from the Father, Who dwells in us by grace, just as the Son and the Holy Ghost."
It is the triune God, therefore, Who dwells in a holy soul, as 1 John 4:16 attests: "God is charity: and he who abides in charity abides in God, and God in him." In John 14:23, Christ similarly professes, "If anyone loves me, he will keep my word, and my Father will love him, and we will come to him and make our abode with him."
Discover how God Himself dwells within a person's soul in season one of Church Militant's Premium show Armor of God—The Holy Spirit and Sanctifying Grace.