Following the flood, the entire human race developed and expanded from a tiny core of just three individuals. The sharp contrast between this small group of brothers and the massive population that followed highlights the complete fulfillment of God's blessing to be fruitful and multiply, resulting in the whole earth being filled [קאסוטו, ביאור יש״ר, ביאור שטיינזלץ]. This blessing of growth applied to all three brothers simply because they were the sons of Noah, even though one of them was wicked [ספורנו].
The focus on exactly three men is not merely a historical fact, but a hint at a fundamental division within humanity. From these brothers emerged three primary archetypes representing the different aspects of human nature [העמק דבר, מלבי״ם, רש ר הירש]. Shem represents spiritual and intellectual individuals who remain close to God. Japheth embodies society, statesmanship, and fair laws. Ham represents simple, material people who are consumed by physical urges and desires. Although they were all born to the same righteous father, they developed in completely different directions. All the diversity and division found in humanity throughout history stems directly from these three roots [רש ר הירש]. Because of this deep connection, the blessings and curses given to these brothers continue to shape and affect all the nations that eventually descended from them [שד״ל].
As humanity grew, they began to populate the globe. The primary approach among commentators is that the people scattered and settled in different regions all over the world [שד״ל, קאסוטו, אוהב גר]. This process involved moving away and breaking apart into small, separate groups [רד״ק, שד״ל, רש ר הירש]. This dispersal also serves as a prelude to the later events of the Tower of Babel, where humanity was famously scattered across the earth [רד״ק, ביאור יש״ר]. However, an alternative perspective suggests that this was not about geographic scattering. Instead, it describes an overwhelming abundance and expansion, much like a spring overflowing its banks. In this view, the earth was simply flooded with a massive, uncountable multitude of human beings [הכתב והקבלה].