The meaning of the trinity has been debated by different sects of Christianity since the organization of the Roman Catholic Church... Here's a brief run down of the events that lead up to it.
Paul converts to Christianity from Judaism, becoming the 2nd founder of Christianity. Takes Judith's place as Apostle after the crucifixion of Christ... Meanwhile, Simon Peter founds the first church of Rome and writes the gospel of Matthew. Chapter 16, verse 19 from the gospel of Matthew serves as the foundation of Roman Catholicism. Both are killed during the reign of Emperor Nero, when Nero persecuted Christians living in Rome.
The period between the founding of Christianity and the reign of Constantine is a dark period for Roman Christians who are persecuted by various Emperors who rule in this time.
Emperor Constantine defeats his rival Maxentius at the battle of Milvian Bridge. The victory prompts him to convert to Christianity (Prior to the battle he had had a "vision" which told him he would win by God's will.) After 313ad Constantine rules the empire jointly with Lycinius and establishes the edict of Milan which legalizes Christianity in the Empire.
Lycinius disagrees with the changes Constantine has been making in the Empire and begins persecuting Christians. Constantine defeats Lycinius in battle and becomes sole ruler of Rome. At this time Constantine institutionalizes the church and begins to assimilate it into the state government, meanwhile St. Jerome translates the bible into Vulgate (The common Latin spoken by the majority of the Empire).
Constantine calls the first ecumenical council of Nicaea. The council addresses the nature of the trinity and of Christ
Now, under Orthodox Roman Catholicism (founded by the apostle Simon Peter) the nature of Christ and the trinity goes like this. The Father, the Son, and the Holy Spirit, are all equally
divine and as such no one is more important or powerful than any other. Jesus has some human nature to him, but both the human (material) and divine (spiritual) nature within him are seen as good. Under Orthodoxy, any belief other than that is considered heresy.
One such "Heretical" sect which was represented at Nicaea were the Arians. Under Arianism, Jesus is seen as a construct, a tool created by God to carry out God's will on earth. This means to the Arians, however, that Jesus is not
divine, and is instead entirely Human in nature.
Another sect, known as Gnosticism, argued that Christ was entirely divine and had no Human nature whatsoever... And a third sect known as Dualism argues that there was a physical and spiritual world. The physical world (Earth) was evil, where as the spiritual world (Heaven) was seen as good. To the Dualists, Jesus was of the physical world, and therefor lived in sin, until he transgressed the physical world to go to heaven.
Under the Orthodox Roman Catholic Church the belief is that The Father, Son, and Holy Spirit are all on an equal level of divinity. The physical world, as well as the spiritual world, are good since both were created by God. And Jesus' human and divine nature, make up equal parts of him, and do not set him apart from the rest of the trinity.
Modern sects of Christianity base their beliefs on Orthodoxy, Arianism, Gnosticism, and Dualism. Which you believe is up to you, and the true nature of the Trinity is up to debate. But if the true nature of the Trinity is intended to be the ideas of the original Apostles, I believe Orthodoxy would be true.
---------- Post added 10-09-2009 at 01:05 PM ----------
"God the Son is separate from God the Father in that God the Son is the finite expression of the infinte."
What does this mean?
I believe this means that, even though God the Son is equally as divine as God the Father, God the Son is the human representation of the Father and as such only represents a small portion of the infinite power that God the Father represents (IE: The son is only a small piece of the whole and infinite essence that is the Father). This could imply that while Jesus is alive and human his power and divinity are both limited until his death when he becomes (or returns) to God the Father.