The Trinity (Latin: Trinitas, lit. 'triad', from Latin: trinus 'threefold') is the Christian doctrine concerning the nature of God, which defines one God existing in three, coeternal, consubstantial divine persons: God the Father, God the Son (Jesus Christ) and God the Holy Spirit, three distinct persons (hypostases) sharing one essence/substance/nature (homoousion).
As the Fourth Lateran Council declared, it is the Father who begets, the Son who is begotten, and the Holy Spirit who proceeds. In this context, one essence/nature defines what God is, while the three persons define who God is. This expresses at once their distinction and their indissoluble unity. Thus, the entire process of creation and grace is viewed as a single shared action of the three divine persons, in which each person manifests the attributes unique to them in the Trinity, thereby proving that everything comes "from the Father," "through the Son," and "in the Holy Spirit."
This doctrine is called Trinitarianism and its adherents are called Trinitarians, while its opponents are called antitrinitarians or nontrinitarians and considered non-Christian by most mainline groups. Nontrinitarian positions include Unitarianism, Binitarianism and Modalism.
While the developed doctrine of the Trinity is not explicit in the books that constitute the New Testament, the New Testament possesses a triadic understanding of God and contains a number of Trinitarian formulas. The doctrine of the Trinity was first formulated among the early Christians (mid-2nd century and later) and fathers of the Church as they attempted to understand the relationship between Jesus and God in their scriptural documents and prior traditions.
Source : Wikipedia