What does 'the earth was divided' in Peleg's days (1 Chronicles 1:19) mean?

That comes from Genesis 10, which 1 Chronicles is repeating. The flood had already occurred some four hundred years earlier, and then in Genesis 10 and 11 you have the Tower of Babel, where they tried to reach heaven with a great, stable tower, which shows they were quite capable about four hundred years after the flood; Peleg died in 2189 BC, and you can see the genealogies of Genesis 5 and 11 laid out year by year in my Luke commentary from the Masoretic, Samaritan, and Septuagint numbers. As they built the tower, God came down and confused their languages, each man speaking differently, and that is the origin of the rudiments of most of our languages, with families like the Romance languages developing later by natural processes. The earth was 'divided' in those days because they had all been one, clustered at Babel, refusing to spread out over the earth as God had commanded, which is itself a kind of refusal to be fruitful and multiply, a serious sin. Once they could no longer speak the same language, they departed from one another, and that division occurred around Peleg's time.