While the word Nephilim is not found in the King James or most other English Bible translations, it does appear in the original Hebrew of the Old Testament. It appears once in the book of Genesis and once in the book of Numbers.
There were giants (nephilim) 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.
And there we saw the giants (nephilim), 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 (Genesis 6:4, Numbers 13:33, KJV)
The original Hebrew word, Strong's Concordance #H5303, is defined as someone who is a feller, meaning a person who is a tyrant or bully. The Brown-Driver-Briggs Hebrew Definitions reference simply translates the word as "giants."
The Land of Giants!
Giants did indeed exist before and after Noah's flood. These large people were especially abundant when the earth was experiencing a population explosion (Genesis 6:1) prior to the deluge. Conservative estimates place the world's population, before it was covered with water, at around one billion!
A common question is who were the "sons of God" who married women and produced children known as the Nephilim. Some believe they were demons who took the form of human flesh and produced giants through human females. This theory does not make any sense, however, since there is no place in Scripture where God calls demons his "sons."
Did They Procreate?
Additionally, there is a giant (pardon the pun) problem with the belief that angels and women were able to produce a race of supersized humans called Nephilim. Scripture says the sons of God took wives for themselves, meaning they were married, and together they produced such children (Genesis 6:2). It does not say these women were somehow raped by angels which subsequently led to them giving birth to giants.
And it came to pass, when men began to multiply on the face of the earth, and when daughters were born to them, that the sons of the mighty ones saw the daughters of men, that they were beautiful; and they took wives for themselves from all whom they chose (Genesis 6:1 - 2, HBFV).
Marriage is a Holy, binding relationship between a man and a woman God instituted in Eden (Genesis 2:24 - 25). There is not even a hint in scripture that He ever spoke about or approved of angelic beings somehow marrying humans and then allowing them to create the Nephilim.
Jesus Reveals the Truth
The possibility of angels and humans marrying and producing giant humans was also indirectly addressed by Jesus. He stated that marriage was a human institution that will not exist after people are resurrected and changed into spirit like the angels (Matthew 22:30). Angelic beings are incapable of marriage and cannot reproduce through procreation.
Then Jesus answered and said to them, "You do err, not knowing the Scriptures, nor the power of God. For in the resurrection they neither marry nor are given in marriage, but they are as the angels of God in heaven (Matthew 22:29 - 30, HBFV).
The Bible informs us, in places other than Genesis, that God's sons are those who have his Holy Spirit dwelling in them (John 1:12, Romans 8:14, 1John 3:2). The nephilim or giants were produced by righteous men who foolishly married worldly women (see Genesis 6:2). Instead of relying on God to guide their marital decisions, these men picked mates they lusted after. They became, as the apostle Paul states, "unequally yoked" with unbelieving women (1Corinthians 7).