How does the Bible describe the different races or people groups of the earth?
After the Flood
When Noah and his family lived, the wickedness of mankind was only bent on doing evil or as it says in Genesis 6:5 “The Lord saw that the wickedness of man was great in the earth, and that every intention of the thoughts of his heart was only evil continually” so God had to judge the world with a coming flood  but since Noah was righteous in God’s sight, Noah and his family would be spared. So “the Lord regretted that he had made man on the earth, and it grieved him to his heart.” So the Lord said, “I will blot out man whom I have created from the face of the land, man and animals and creeping things and birds of the heavens, for I am sorry that I have made them” (Gen 6:6-7). After God judged the world, the world would have to be repopulated and that is why it says that “God blessed Noah and his sons and said to them, ‘Be fruitful and multiply and fill the earth’” (Gen 9:1).
The Sons of Noah
After the flood was over, “The sons of Noah who went forth from the ark were Shem, Ham, and Japheth. (Ham was the father of Canaan.) These three were the sons of Noah, and from these the people of the whole earth were dispersed” (Gen 9:18-19). After Noah was found by his son Ham lying naked from drunkenness, “Noah awoke from his wine and knew what his youngest son had done to him, he said, Cursed be Canaan; a servant of servants shall he be to his brothers” (Gen 9:24-25). Now Canaan or the descendants of Ham, who would be the Canaanites, would be serving his brothers, Shem and Japheth when they became a nation. True to his curse, Ham had a son named Nimrod and as it was written, “He was a mighty hunter before the Lord. Therefore it is said, “Like Nimrod a mighty hunter before the Lord” (Gen 10:9) and this was the beginning of the kingdom of Babel (Gen 10:10). In Genesis chapter 10 you can see all of “the clans of the sons of Noah, according to their genealogies, in their nations, and from these the nations spread abroad on the earth after the flood” (Gen 10:32) through “the sons of Ham, by their clans, their languages, their lands, and their nations” including Shem and Japheth, but they would have remained there, in one place, and been of one language and one nation if God did not scatter them and that is exactly what He was going to do.
The Tower of Babel
Nimrod was defiant against God as it said he was a “mighty hunter before the Lord” (Gen 10:10) which means he was despising God by ruling a nation in unrighteousness and trying to build a tower to heaven, thereby hoping to bypass God in getting to His throne. Most people might not realize the wickedness of this man. He forced pagan religious practices, just a generation removed from his father Ham and his grandfather, Noah, so he must have known there was a God and that He is sovereign over mankind but Nimrod  wasn’t about to bow the knee. In defiance, the nation of Babel collectively said, “Come, let us build ourselves a city and a tower with its top in the heavens, and let us make a name for ourselves, lest we be dispersed over the face of the whole earth” (Gen 11:4). When God saw that all the people of the earth were joining forces together, God said “Behold, they are one people, and they have all one language, and this is only the beginning of what they will do. And nothing that they propose to do will now be impossible for them. Come, let us go down and there confuse their language, so that they may not understand one another’s speech” (Gen 11:6-7). God had no choice but to disperse “them from there over the face of all the earth, and they left off building the city. Therefore its name was called Babel, because there the Lord confused the language of all the earth. And from there the Lord dispersed them over the face of all the earth” (Gen 11:8-9). So the children of Ham, Shem, and Japheth spread out across the face of the earth since many of the people groups could no longer understand one another’s language.
Many but One
I don’t believe in races…I believe in graces for people. For the believer in Christ it is as the Apostle Paul wrote; “there is not Greek and Jew, circumcised and uncircumcised, barbarian, Scythian, slave, free; but Christ is all, and in all” (Col 3:11) because God “made from one man every nation of mankind to live on all the face of the earth, having determined allotted periods and the boundaries of their dwelling place” (Acts 17:26), something he would write to the Galatians, “There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus” (Gal 3:28). Not only does God appoint rulers of the nations, he gives boundaries and limits to them (Psalm 148:11; Prov 21:1; Rom 13:1) so they are where they are by God’s decree. To God, “a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter” (Rom 2:29) so God never looks at skin color but at the heart (1 Sam 16:7). We are all descendants of Adam (1 Cor 15:45).
Races are a human invention. This is not to deny the existence of nations or national boundaries or people of differing skin color but that’s only physical and doesn’t really mean anything to God, because it’s not race but grace that God is interested in giving. We all bleed red blood because God made man from one man and He made “every nation of mankind to live on all the face of the earth” (Acts 17:26) so there is no race but the human race and the race that we run with endurance. Near the end of Paul’s life, he could honestly say “I have fought the good fight, I have finished the race, I have kept the faith” (2 Tim 4:7). “God does not show favoritism, but in every nation anyone who fears him and does what is right is acceptable to him” (Acts 10:34-35). We all matter, regardless of language, national origin, or skin color. God “shows no partiality to princes, nor regards the rich more than the poor, for they are all the work of his hands” (Job 34:19) so neither should we show partiality or prejudice.
Read more about Babel in the Bible: Tower or Babel Bible Story Summary 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.