The Christian doctrine of the Trinity teaches the unity of Father, Son, and Holy Spirit as three persons in one Godhead.
By 'trinity' is meant 'three in one' and 'one in three', not 'tri-theism' or 'three Gods'.
The Holy Spirit is believed to dwell in the individual believers and enable them to live a righteous and faithful life.
The trinity was not an expressed part of Christian teaching until about 300 A.D. when Arius, a Christian leader in Egypt, and others were teaching Christ was created by God and distinct from him. At the First Council of Nicea a central concern among Church leaders was that the holiness of Jesus be regarded and reinforced in teaching.

The concept of the Trinity was dropped during the 18th century enlightenment.
See Deism in England and France in the 18th century - Wikipedia

The most common Biblical references for the concept of a trinity are from Christ's "great commission" to the disciples in Matthew 28:19, 'Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,'
Others quote [John 1:1],
"In the beginning was the Word, and the Word was with God, and the Word was God."
and [Isaiah 9:6],
For to us a child is born, to us a son is given, and the government will be on his shoulders.
And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace.

and from Paul's letters. In Ephesians 2:18 he says 'For through Him (Christ) we both (Jew and Gentile) have access to the Father by one Spirit'.

It is generally accepted that it was established at the First Council of Nicaea with the Nicean Creed which in part states "We believe in one Lord, Jesus Christ, the only Son of God, eternally begotten of the Father, God from God, Light from Light, true God from true God, begotten, not made, of one Being with the Father."

There are a number of legends about the First Council of Nicaea (325AD) in circulation on the internet. One is there were votes on the trinity and other concepts. See The Council of Nicaea (Nicea) and the Bible which tries to get to the truth.

Augustine of Hippo (354-430):
Augustine's "On the Trinity", in which he developed what has become known as the 'psychological analogy' of the Trinity, is also among his masterpieces, and arguably one of the greatest theological works of all time.
The mind, consisting of memory, understanding, and will, reflected the imago Dei, in Trinitarian form. Just as the Father, Son, and Holy Spirit, were One, with one mind, so too was the humanmind one, though with three distinct aspects.
See Augustine

A Spanish physician, Michael Servetus, studied the Bible and concluded that the concept of the Trinity, as traditionally conceived, was not biblical. His books On the Errors of the Trinity and Christianismi Restitutio caused much uproar. Servetus was eventually arrested, convicted of heresy, and burned at the stake in Geneva in 1553 under the order of John Calvin. Source: Michael Servetus Burned for Heresy - 1501-1600 Church History Timeline

See also:
Understanding the Trinity
Trinity and Deity of Christ at LetUsReason.org
Bible Topics: Christ is God
Criticism

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