What I understand of the Trinity is this:
God = Father
God = the Son, Jesus Christ
God = Holy Spirit
I have posted this before and no one has told me that this is not what means. If this is not what it is then maybe you can tell me what it means? I have never heard of modalism.
The Trinity is something like this:
When someone says, "God," it is naturally assumed they are referring to one specific person.
Trinity doesn't see it this way.
Rather, Trinity re-envisions God to refer to three distinct persons without resorting to the plural, "Gods".
This, however, differs from polytheism in that these three persons are indistinguishable in their intentions, will, agenda, whatever.
In other words, unlike in polytheism, you cannot pit Jesus against Father or Holy Spirit. They won't oppose one another.
They operate as a single entity, but remain three distinct people.
Take a flock of birds flying in the air, for example.
When they turn, they do not curve around, each staying behind the one in front. Rather, they turn their bodies, and those birds on the side become the new leaders.
Their flight is not consciously coordinated, but they instinctively think like a single organism, though they remain unique from one another.
Michael Crichton, for example, used this theory about birds as the basis for his Velociraptors in his novel, "Jurassic Park."
Therefore, when a Trinitarian says, "God," they are not referring to a single person, but a three-fold flock of people that operate as a single hybrid entity.
In this way, they get around the verses that distinguish Jesus as a unique person from the Father while getting to maintain that they are both God.
However, in those verses that distinguish between Jesus and God, I've found that Trinitarians simply don't read THOSE verses at face value.
For example, take a verse that has come up a lot on this thread: John 1:1
It says, "The Word was with God, and the Word was God."
Trinitarians strongly emphasize the bit where it says the Word (which turns out to be Jesus) was God, but tend to skip or redefine the first part, where it says the Word (which turns out to be Jesus) was with God.
Now, if it said, "was with the Father," Trinitarianism would do just fine. However, the verse says God, not Father.
So, the following logic--
The Word was with God.
The Word became flesh.
Therefore, someone who had been with God became flesh.
Therefore, Jesus doesn't seem to have been God.
--gets overlooked, while the logic--
The Word was God.
The Word became flesh.
Therefore, God became flesh.
Therefore, Jesus is God.
--gets insisted upon.
Anyway, that's Trinitarianism.
Three people=one God.
Modalism, on the other hand, says that there is only one God who simply revealed himself throughout history in the forms of three different people, but was actually, all along, just one person. Hence, Jesus, Father and Holy Spirit never exist at the same time, but one after the other.
A modalist, for example, has a problem with Jesus praying to his Father. Since they are actually the same person, Jesus is really just praying to himself.
Anyway, that's modalism.
One God=Three modes.
While I think modalism is not such a great explanation, the Trinity draws an interesting picture of the eternal relationship between Jesus and God. So, while I am not convinced that Jesus is God in the strictest sense, I do think the Trinity is the best explanation available for what the New Testament is trying to explain to us.
There are those 62 verses that seem to indicate that Jesus is God. And, there are a substantial number of verses that explicitly distinguish Jesus from God (Hebrews 2 is a great example).
The strongest argument, however, seems to be that the Bible isn't clear on whether or not Jesus is God, and that any conclusion on this matter is an issue of personal conviction. I am personally convinced that the Gospel was meant to instill us with confidence that Jesus was a willing and able Savior and Lord whether or not he turns out to be God.
Anyway, I hope this helps.