The term "Nephilim" occurs twice in the Hebrew Bible, both in the Torah. The first is Genesis 6:1-4, immediately before the story of Noah's ark:
1. When men began to increase in number on the earth and daughters were born to them, 2. The sons of God saw that the daughters of men were beautiful, and they married any of them they chose. 3. 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." 4. 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.
The second is Numbers 13:32-33, where the Hebrew spies report that they have seen fearsome giants in Canaan:
32. 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."
Ezekiel's "mighty fallen": nephilim as ancient warriors
Ezekiel 32:27 speaks of "the fallen mighty (gibborim nophelim, גִּבֹּורִים נֹפְלִים) of the uncircumcised, which are gone down (yaradu, יָרְדֽוּ) to the grave with their weapons of war"; a change to the vowels would produce the reading gibborim nephilim.
Numbers and Amos: Nephilim as giants
In Amos 2:9, while not using the word "nephilim", Yahweh reminds the prophet that he "destroyed the Amorites before you, whose height was as the height of cedar trees". Genesis 6:4 says "the nephilim were on the earth in those days (before the Flood), and also after", and most later compositions and translations, including the Septuagint, therefore understand the nephilim to be giants.
Ambiguity in Genesis 6:4
The nature of the nephilim is complicated by the ambiguity of Genesis 6:4, "the sons of God joined with the daughters of mankind, who bore them children - they were the ancient warriors, the men of renown", which leaves it unclear whether they are the "sons of God" or their offspring who are the "ancient warriors". Richard Hess in The Anchor Bible Dictionary takes it as read that the nephilim are the offspring, as does P. W. Coxon in Dictionary of deities and demons in the Bible.