The Nephilim are fallen Angels, or descendants of such.
First we need to understand that the "sons of God" mentioned in Genesis are angels, and here's how we do that. The Hebrew words used here are Ben 'elohiym.
Ben Literally means a 'descendant of'. So sons, grandsons, translated to son.
'elohiym can be translated into a few different words. rulers, judges, divine ones, angels, gods.
You can see that the scholars behind the NKJV have translated these words to say "sons of God", while the new international version scholars have translated the meaning to say "the angels."
Satan presents himself with the other angels
We know that Satan is an angel and we see him presenting himself with the other angels before God, in the book of Job.
Job 2:1 NKJV
Again there was a day when the sons of God came to present themselves
before the LORD, and Satan came also among them to present himself
before the LORD.
Job 2:1 NIV
On another day the angels came to present themselves before the
LORD, and Satan also came with them to present himself before him.
We shall be called sons of God, equal to Angels
We can also expand on this understanding with the following verses, in order to know for sure that these sons of God are spiritual beings filled with the holy spirit.
Luke 20:36 NKJV
nor can they die anymore, for they are equal to the angels and are
sons of God, being sons of the resurrection.
Romans 8:14 KJV
For as many as are led by the Spirit of God, they are the sons of God.
These particular angels in Genesis are fallen Angels
Genesis 6:4 NIV
The Nephilim were on the earth in those days—and
also afterward—when the sons of God went to the daughters of humans
and had children by them. They were the heroes of old, men of renown.
The Hebrew word for Nephilim is N@phiyl which originates from the word Naphal which means "to fall, fallen."
We can see further connection and description of these fallen angels in Numbers
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.”
These three men seemed to have lived for a long time, as we see their lives spanning past the exodus, when they were finally driven out of their land and we don't hear about them anymore.
And they gave Hebron to Caleb, as Moses had said. Then he expelled
from there the three sons of Anak.
This gives us a lot of insight into Genesis 6:3, when God says that His spirit shall not strive with man forever. He will shorten the life of mortal men to 120 years.
Genesis 6:3 (NKJV)
3 And the LORD said, “My Spirit shall not strive with man forever, for
he is indeed flesh; yet his days shall be one hundred and twenty
It seems clear to me that God is talking about these fallen angels when He says "My Spirit."