Catechism of the Catholic Church
2794 This biblical expression does not mean a place ("space"), but a way of being; it does not mean that God is distant, but majestic. Our Father is not "elsewhere": he transcends everything we can conceive of his holiness. It is precisely because he is thrice holy that he is so close to the humble and contrite heart.
"Our Father who art in heaven" is rightly understood to mean that God is in the hearts of the just, as in his holy temple. At the same time, it means that those who pray should desire the one they invoke to dwell in them. 54
"Heaven" could also be those who bear the image of the heavenly world, and in whom God dwells and tarries. 55
2795 The symbol of the heavens refers us back to the mystery of the covenant we are living when we pray to our Father. He is in heaven, his dwelling place; the Father's house is our homeland. Sin has exiled us from the land of the covenant, 56 but conversion of heart enables us to return to the Father, to heaven. 57 Jn Christ, then, heaven and earth are reconciled, 58 for the Son alone "descended from heaven" and causes us to ascend there with him, by his Cross, Resurrection, and Ascension. 59
2796 When the Church prays "our Father who art in heaven," she is professing that we are the People of God, already seated "with him in the heavenly places in Christ Jesus" and "hidden with Christ in God;" 60 yet at the same time, "here indeed we groan, and long to put on our heavenly dwelling." 61
[Christians] are in the flesh, but do not live according to the flesh. They spend their lives on earth, but are citizens of heaven. 62
2797 Simple and faithful trust, humble and joyous assurance are the proper dispositions for one who prays the Our Father.
2798 We can invoke God as "Father" because the Son of God made man has revealed him to us. Jn this Son, through Baptism, we are incorporated and adopted as sons of God.
2799 The Lord's Prayer brings us into communion with the Father and with his Son, Jesus Christ. At the same time it reveals us to ourselves (cf. GS 22 § 1).
2800 Praying to our Father should develop in us the will to become like him and foster in us a humble and trusting heart.
2801 When we say "Our" Father, we are invoking the new covenant in Jesus Christ, communion with the Holy Trinity, and the divine love which spreads through the Church to encompass the world.
2802 "Who art in heaven" does not refer to a place but to God's majesty and his presence in the hearts of the just. Heaven, the Father's house, is the true homeland toward which we are heading and to which, already, we belong.
English Translation of the Cathechism of the Catholic Church for the United States of America © 1997, United States Catholic Conference, Inc.