The creeds teach that God is Trinity. The English word used to distinguish the three is “person.” The doctrine of the Trinity states that the one God who created the world exists, from eternity, in three persons: the Father, the Son and the Holy Ghost, who are united in one substance of being.
A note: The word “substance” comes from the Greek word, homoousious, which means “one substance” or “one essence.” At the Council of Nicea in 325, the Arians (those who did not believe that Jesus is God) taught that Jesus was of “like substance” or “homoiousious” with the Father. Thus, the difference between orthodoxy and heresy was one Greek vowel, the “i”, or iota.
One way to understand the Trinity is provided by the Church father, St. Augustine. He pointed out that a relationship of love requires three: a lover, a beloved and love itself. The Father loves the Son, the Son loves the Father and the Holy Ghost is the personification of their love (cf. Romans 5:5). Thus, God is love because He is, within His own being, a loving relationship. He is not merely an abstract principle of love.
God created the world because of His desire to share His love with created beings. Love is also the motive for the cross (St. John 3:16). By contrast, a unitarian god might create out of a need for someone to love. Indeed, pagan stories taught that the god created or acted out of need or malice. The Bible and the creeds reveal one God whose motive is love.
All Christian theology builds upon these two cardinal doctrines: Jesus is fully God and fully man. And God is Trinity. Errors with regard to these doctrines are called, in classical Christian terms, heresies.