The following is written in the Old Testament of the Bible, the book of Genesis:
"When men began to increase in number on the earth and daughters were born to them, the sons of God saw that the daughters of men were beautiful, and they married any of them they chose. Then the LORD said, 'My Spirit will not contend with man forever, for he is mortal; his days will be a hundred and twenty years.' 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."1
There are Bible scholars who believe that the "sons of God", spoken of in the above verses, is referring to fallen angels; in Scripture, the term "sons of God" is often used in reference to angels. Their belief is that the Nephilim (definition: the fallen ones) were a race of giant demigods produced by the unnatural cohabitation between women (the daughters of men) and fallen angels (the sons of God.) Early Jewish scholars, as well as the early Christian Church, held this view; around the 4th century AD, however, other views were put forth.
There is also the belief that the "sons of God", mentioned in the above verses, is referring to the Godly line of Seth; the "daughters of men" is referring to the ungodly line of Cain (Cain is the son of Adam and Eve who killed his brother Abel.)
As to which view is correct, it's important to remember that angels are not able to procreate (reproduce.) If the "sons of God" is referring to fallen angels, then what occurred would have to be referring to demon possession; demons are fallen angels.
1 (Genesis 6:1-4 NIV)