As one of the comments stated, in order to understand why Christians believe Jesus to be the 'Son of God', you'll want to grasp the concepts of the Incarnation of the Logos (God's Word, also sometimes referred to as the 'Wisdom of God' assuming flesh). And the trinity, which is the concept that there are three Persons in a single being. This is a difficult thing for most of make sense out of and explain accurately. I have heard this explained that God's thoughts are so perfect that being aware of Himself actually constitutes a Second Person. In other words, His wisdom is so Perfect it itself becomes a Person. These two Persons Love one another so Perfectly that that Love itself also is a Third person. All three are still of the same being, constituted by the same 'beingness' and drawing upon the same source of power. This is how God can be 3 Persons but still 1.
A man named St. Thomas Aquinas gave an analogy to explain how in the world God could assume a human form: It's LIKE (and not the same as) when you have a dream, the entire dream world is a product of your thoughts. You yourself assume the limitations of this dream world and enter it and experience it. Since God thought the world into existence, its kind of LIKE God did something similar.
The documents of the New testament detail the life and teachings of Jesus; in which He claims quite explicitly that He is one with the Creator. There are hints in the Old testament that support this concept. Jesus' claim to be God is why He was singled out for Crucifixion by His own people; where as other people who claimed to be the Messiah weren't: nobody else made such a claim. And without such a claim, why would His own people want Him dead? Christians have to decide their answer to this dilemma: Either Jesus was crazy, a deceiver or exactly what He said He was.
The title Son of God is used for a few reasons. In our sacred scriptures, having a son means passing on one's own nature. Therefore, to be the Son of God is possess the same nature as God. Since the body of Jesus was conceived by the power of God (and not by a sexual act, since God has no physical body), you could also say Jesus is a Son in this way. There are other reasons too, but this is getting a bit long.
I hope this helps, I know I said a lot for background's sake. For a better explanation on the Trinity, I'd look at some stuff by Father Mike Spitzer. I am reciting from memory his explanations; but reading it yourself may be clearer.