Catechism of the Catholic Church
249 From the beginning, the revealed truth of the Holy Trinity has been at the very root of the Church's living faith, principally by means of Baptism. It finds its expression in the rule of baptismal faith, formulated in the preaching, catechesis and prayer of the Church. Such formulations are already found in the apostolic writings, such as this salutation taken up in the Eucharistic liturgy: "The grace of the Lord Jesus Christ and the love of God and the fellowship of the Holy Spirit be with you all." 81
250 During the first centuries the Church sought to clarify her Trinitarian faith, both to deepen her own understanding of the faith and to defend it against the errors that were deforming it. This clarification was the work of the early councils, aided by the theological work of the Church Fathers and sustained by the Christian people's sense of the faith.
251 In order to articulate the dogma of the Trinity, the Church had to develop her own terminology with the help of certain notions of philosophical origin: "substance", "person" or "hypostasis", "relation" and so on. In doing this, she did not submit the faith to human wisdom, but gave a new and unprecedented meaning to these terms, which from then on would be used to signify an ineffable mystery, "infinitely beyond all that we can humanly understand". 82
252 The Church uses (I) the term "substance" (rendered also at times by "essence" or "nature") to designate the divine being in its unity, (II) the term "person" or "hypostasis" to designate the Father, Son and Holy Spirit in the real distinction among them, and (III) the term "relation" to designate the fact that their distinction lies in the relationship of each to the others.
English Translation of the Cathechism of the Catholic Church for the United States of America © 1997, United States Catholic Conference, Inc.