‘The Nephilim were on the earth (or “in the land”) in those days, and also afterwards, when the sons of God came in to the daughters of men, and they bore children to them. These were the mighty men that were of old, men of renown.'
The position of this verse in the narrative (we might expect it before Genesis 6:3), and the fact that it is not connected by the usual ‘waw' (‘and') to the previous verse, suggests that this may be a word of explanation put in by the compiler (compare the explanatory note in Numbers 13:33). He knows his readers may be puzzled by the reference to the ‘sons of God' so he explains, ‘the ‘nephilim' were on the earth in those days'. He is thus connecting what is happening with the ‘nephilim', a term which he knows his readers will recognise. The nephilim might mean ‘the fallen ones' (from naphal - to fall), which would tie in with seeing the sons of God as ‘fallen angels'.
“In those days” refers to the time of the demonic ‘marriages' and to God's severe warning to mankind.
But worse is to follow, for ‘afterwards', i.e. after God's warning, the position deteriorated and these nephilim, these ‘sons of God', with the connivance of the daughters of men, continued their unholy alliances and this resulted in children being born with special ‘fallen' powers which enabled them to become famous. These also were seen as ‘nephilim' (compare Numbers 13:33 ‘the nephilim which come of the nephilim').
The idea here is probably that the women were married to humans, but that their occult practises resulted in the children born of these human marriages being somehow ‘infected' by their demonic partners. The phrase ‘came into -' regularly refers to intercourse, and this stresses the deeply personal depth of demonic experience into which these women threw themselves. It further explains why the destruction of all living beings was required.
Some who have connected with the occult in depth in modern days can testify to those who have gone through such experiences with their demon ‘lovers'. This was evil of an extreme kind and demonstrates why the flood was necessary. Indeed without this explanation we might have questioned whether it was not rather severe, given God's earlier mercy to Cain. But the fact is that mankind, at least in this part of the world, had freely and willingly sunk to a depth of evil beyond our wildest imaginations.
As referred to already there is a further reference to the nephilim in Numbers 13:33, which demonstrates the awe with which the term was then viewed. This suggests that the word had by then gained the meaning of ‘mighty men' or ‘giants' and was thus applied to any excessively huge men (not necessarily connected with the original ‘nephilim), especially the sons of Anak, who clearly had gained a reputation and were seen as the product of special descent. We may surmise that by that time the word ‘nephilim' had become a word which expressed superstitious fear, whereby any huge men were connected with other worldly powers, especially when they were opponents. The Genesis story was known to them and they assumed that something similar had caused these men to be ‘gigantic', i.e. larger than normal, which increased their fear of them.