He lived at the time of the Arian heresy, which claimed that Jesus was a creature of God; the first creature, but definitely not God. Arianism was condemned in A.D. 325, but even when St. Gregory was made bishop in 371 it was still a serious problem. Emperor Theodosius called for a council in 381 to address the continuing problem. St. Gregory was a great proponent for the truth of the faith, that Jesus is consubstantial with the Father, and that the Holy Spirit is also consubstantial with the Father and the Son. In other words, he defended the truth of the Trinity, the greatest mystery of our faith.
We are not called to “understand” the mystery of the Trinity. Faith calls for trust. We trust that what we have been taught about God is true, because of who taught us, Jesus Christ. Jesus said that God is his Father. God is our Father, too, but not in the same way. Jesus is God. The Father is God. The Holy Spirit is God. We don’t explain it with a scientific or mathematical proof. We believe it, like we believe in love. St. Gregory of Nyssa, pray for us.