The Christian origin of the holiday is that it falls on the days before the feast of All Hallows, which was set in the eighth century to attempt to stamp out pagan celebrations. Christians would honour saints and pray for souls who have not yet reached heaven.
The Americanised (Americanized?) Halloween that we experience today actually originated in the Celtic fringes of Britain, and was adapted over the decades by Christian traditions, immigrants conventions and an insatiable desire for sweets.
The tradition of Halloween was carried to America by the immigrating Europeans. Some of the traditions changed a little, though. For example, on Halloween in Europe some people would carry lanterns made from turnips. In America, pumpkins were more common. So people began putting candles inside them and using them as lanterns. That is why you see Jack o lanterns today.