The Nephilim

“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.” Genesis 6:4
We read of the Nephilim on two general occasions in the Bible. The first is before the Flood of Noah (and, it seems, was one of the reasons God brought the Flood in the first place). The second is “also afterward” – when the Israelites entered the land of Canaan (Num. 13:33).
So what do we know about them? They were giants. We read of Goliath, who was 9 feet tall (1 Sam. 17:4), a Rephaite (see 2 Sam. 21:15-22 and 1 Chr. 20:4-8). We read of Og, the king of Bashan, who was also a Rephaite, whose bed was 13 feet long (Deut. 3:11). Thus the Rephaites, or Rephaim, were one of the Nephilim tribes. The Anakites (or Anakim, the descendants of Anak) were another (Deut. 13:28, 33).
The word ‘Nephilim’ comes from the Hebrew word naphal which means ‘to fall’. Thus the Nephilim were the ‘fallen ones’. They were produced, we are told, “when the sons of God went to the daughters of men and had children by them.” There is only one group in the Old Testament who are called the ‘sons of God’ – the bene Ha Elohim - and that is angels. (See Job 1:6, 2:1, 38:7.) Clearly these are fallen angels, for godly angels would not engage in this kind of sin, corrupting the human race. Jude and Peter refer to them in Jude 1:6 and 2 Pet. 2:4-5. Thus the Nephilim were the offspring of fallen angels and human women.
This also explains why God chose Noah and his family. We read “Noah was a righteous man, blameless among the people of his time” (Gen. 6:9). What the Hebrew actually says is that he was ‘perfect in his generations’. His genealogy had not been corrupted by these activities. And so God spared him through the flood, and used him to start the human race all over again. This also explains why the Israelites were instructed to kill every many, woman and child of these tribes in Canaan. God did not want the gene pool of His people, from whom He had promised the Messiah would come, to be corrupted by fallen angels.

This is a controversial topic, and there will be many who disagree. But if you would like to read more, I can recommend the following:
E.W. Bullinger, ‘The Companion Bible’, Appendix 23 and Appendix 25.