Question:
What is the Trinity? 

Answer:
234 The mystery of the Most Holy Trinity Faith is the central mystery of Christian faith and life. It is the mystery of God in himself. It is therefore the source of all the other mysteries of faith, the light that enlightens them. It is the most fundamental and essential teaching in the “hierarchy of the truths of faith.” The whole history of salvation is identical with the history of the way and the means by which the one true God, Father, Son and Holy Spirit, reveals himself to men “and reconciles and unites with himself those who turn away from sin.”

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.”

262 The Incarnation of God’s Son reveals that God is the eternal Father and that the Son is consubstantial with the Father, which means that, in the Father and with the Father the Son is one and the same God.

263 The mission of the Holy Spirit, sent by the Father in the name of the Son (John 14:26) and by the Son “from the Father” (John 15:26), reveals that, with them, the Spirit is one and the same God. “With the Father and the Son he is worshipped and glorified.” (Nicene Creed).

265 By the grace of Baptism “in the name of the Father and of the Son and of the Holy Spirit,” we are called to share in the life of the Blessed Trinity, here on earth in the obscurity of faith, and after death in eternal light.
From the Catechism of the Catholic Church