“To Eber were born two sons: the name of one was Peleg, for in his days the earth was divided” (Gen 10:25)
“Two sons were born to Eber. One of them was named Peleg because the earth was divided during his lifetime, and the namer of his brother was Joktan” (1 Chr 1:19).
What does it mean that “the earth was dividing” during the lifetime of Peleg?
Some think it could mean that it was physically divided with a continental drift. This is a possibility and would explain the indigenous people of the Americas. But it is not known for sure and not much is made of this as one would expect.
The more likely meaning is that this was the tower of Babel incident, where the Lord imparted language and the people divided. The key is the descendants of Shem.
Shem had sons, predominantly Peleg and Joktan. Joktans descendents moved eastward to Babylon area (Gen 10:30-31). Then after the tower of Babel incident again we have a geneology of Shem, but this time following the line through Peleg and ultimately to Abraham. What we then see is the two divergent lines of humanity–East and West.
