Nobody knows for certain. The word appears in just two passages. Genesis 6 mentions them alongside the "sons of God" marrying human women before the flood, and Numbers 13 has frightened spies claiming to have seen them in Canaan. The KJV calls them "giants" because the Greek translation did. Who they were depends on who the "sons of God" were, and Christians have given three answers to that since the earliest centuries.
Two verses. That is all the Bible says about them by name.
There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.Genesis 6:4 — "giants" is the KJV's word for the Nephilim
And there we saw the giants, the sons of Anak, which come of the giants: and we were in our own sight as grasshoppers, and so we were in their sight.Numbers 13:33 — said by the spies the next verse calls an "evil report"
Read Genesis 6:4 slowly. It says the Nephilim were on the earth "in those days, and also after that", at the time the sons of God had children. It does not quite say the Nephilim were those children. Whether they were is part of the question.
Numbers 13 raises another puzzle. If the Nephilim lived before the flood, how are there any in Canaan afterwards? The text puts the claim in the mouths of spies who are trying to talk Israel out of entering the land, so it may be their fear speaking rather than a fact the narrator endorses.
The confidence marks matter most here, because this is a subject where speculation travels faster than evidence.
The common mistake is to talk about the Nephilim as if the Bible gave a description of them. It does not. Everything about their size comes from the Greek word "giants" and from frightened spies, and the rest comes from later books like 1 Enoch.
The opposite mistake is to wave the angel reading away as fringe. It is the oldest reading on record, and it was the majority view in the early church before Augustine. You can disagree with it, but it is not a modern novelty.
The question underneath is who the "sons of God" are. The same phrase means angels in Job 1:6 and 38:7, which is the strongest argument for the oldest reading. Whether it means the same thing in Genesis 6 is exactly what readers still disagree about.