Nephilim: Genesis 6:1-7

The Nephilim were on the earth in those days—and also afterward—when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.

This is one of the great mysteries of the Bible. They are also mentioned in the book of Numbers:

Then Caleb silenced the people before Moses and said, "We should go up and take possession of the land, for we can certainly do it."  But the men who had gone up with him said, "We can't attack those people; they are stronger than we are."  And they spread among the Israelites a bad report about the land they had explored. They said, "The land we explored devours those living in it. All the people we saw there are of great size. 33 We saw the Nephilim there (the descendants of Anak come from the Nephilim). We seemed like grasshoppers in our own eyes, and we looked the same to them." 

Numbers 13:30-33 NIV

Anyone who doesn't think the Bible is filled with Mystery should consider Gen. 6.  I don't think anyone can adequately explain Genesis 6:1-7. But I'd love to try to draw a few conclusions.  The Bible is too mysterious and inexplicable to be false. There is a mystery of the spirit world. God places warning signs all over the Bible about the dangers of the worship of angels and (of course) demons. He's saying, "Guard your heart and mind from any spiritual interaction that doesn't find a direct connection to God. We don't need a bridge to Jehovah other than Christ.