The Nephilim are mentioned in Genesis 6:1-4,
When man began to multiply on the face of the land and daughters were born to them, the sons of God saw that the daughters of man were attractive. And they took as their wives any they chose. Then the Lord said, “My Spirit shall not abide in man forever, for he is flesh: his days shall be 120 years.” The Nephilim were on the earth in those days, and also afterward, when the sons of God came in to the daughters of man and they bore children to them. These were the mighty men who were of old, the men of renown. (Gen. 6:1-4)
A lot of people say that these are giants. Some people even say that they're fallen angels who married human beings. In Numbers 13:33, they're described as fierce, as large in size compared to the Israelites, who look like grasshoppers in comparison. In Ezekiel 32:27 they're described as terrifying warriors. Here's the thing, fallen angels and married women cannot come together and reproduce. They can't create a hybrid race. Jesus tells us in Mark 12:25 that the angels don't reproduce. They don't even have bodies.
Go back a couple of chapters to Genesis 4; the murderous Cain builds his proud city with a long list of descendants marked by their contributions to civilization. Then in verse 26, you get to Seth, who replaced Abel. In contrast with that long line of accomplished children of Cain, Seth’s line is described in one sentence: “then people began to call on the name of the Lord.” So, you have that war between the seed of the serpent, Cain, in this instance, and the seed of the woman, the Messiah, who is going to come from Seth’s line. Satan failed to intercept the Messianic line by enticing Cain to kill Abel. So, what does he do now? He tries a different tack: corrupt the Messianic line by enticing the sons of God, that is Seth’s descendants, to intermarry with Cain’s descendants. The result was a group of apostates, like their forbearer, they were cruel and murderous tyrants.
Apostasy means to abandon the faith, to reject the gospel, the good news. You see that all the way back with Cain. After the Fall, there was a need for not just a tribute offering, the kind of offering that a loyal subject brings to a king to say "thank you for letting me live on your land," but rather a sacrifice for sin. And an atoning sacrifice without the shedding of blood, there is no forgiveness. Well Cain brought produce of the land. He was a produce farmer and so he brought cucumbers and squash and God wasn't pleased with that sacrifice because basically he came saying "I don't need an atoning sacrifice. I don't need a substitute for my sins." Whereas Abel brought the sacrifice that God required, which pointed forward to the Lamb of God who takes away the sin of the world. Essentially, when God was displeased with Cain's sacrifice he became jealous and he became the first persecutor of the Church of God. What follows this episode of the Nephilim is the story of Noah and the flood and now it all sort of makes sense. God's wiping out the apostates from his church, whittling it down to Noah and his family.
The Nephilim episode reminds us then of a few things. First, the ever-present danger of apostasy which includes the inter-marrying of believers with unbelievers, Satan still uses that one. Second, this reminds us that God kept his promise of sending the Messiah, in spite of Satan's untiring attempts to intercept them along the way. And third, it reminds us of Jesus' promise in Matthew 16:18, "I will build my church, and the gates of hell will not prevail against it."
Adapted from an answer given in Episode 122 of the Core Christianity Radio Show.