Why is it important for people who believe in Trinity that Jesus is God? I've heard a lot of discussion lately about whether Jesus is God, or not. I know there are arguments for Trinity, and arguments against. But I am wondering, why is it so important for those who believe in Trinity that Jesus is also God, and not only a perfect human being?
The main reason that it is important to Protestants, that Jesus is the son of God, is because that is the basic precept on which their salvation depends. If Jesus were not deity, (or God) he could not keep the promises he made concerning salvation.
All Scripture is quoted from the King James translation.
example:

John 10:15 through 18  As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep. And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, and one shepherd. Therefore doth my Father love me, because I lay down my life, that I might take it again. No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.

In the above passage what you will find, is that Jesus has promised that he will give salvation to his sheep. Jesus used the example of a shepherd because the people were familiar with sheep herding, and he also referred to those being saved as his sheep.
But the really important part is the part about his laying down his life and being able to take it up again.
If Jesus did not have the power to take up his own life again, how would he ever have the ability to give eternal life to anyone else?

John 10:28  And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.
John 6:54  Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day.

Unless Jesus were God and not just a good man all of these would be hollow promises, since salvation is of God:

Luke 3:6 And all flesh shall see the salvation of God.

The veracity of Jesus claim is found in the Old Testament. Particularly in the Book of Isaiah, which is most descriptive, and also in many other Prophets from many years before his birth, which is foretold in Isaiah chapter 7:

John 5:39  Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me.
Isaiah 7:13 and 14 And he said, Hear ye now, O house of David; Is it a small thing for you to weary men, but will ye weary my God also? Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.

Finally; if Jesus were not God all who have put their trust in Jesus for their Salvation would still be lost with no hope of eternal life.

John 6:37  All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out.

Mark 2:17 When Jesus heard [it], he saith unto them, They that are whole have no need of the physician, but they that are sick: I came not to call the righteous, but sinners to repentance.
Luke 19:10 For the Son of man is come to seek and to save that which was lost.