This story can be found in Genesis 11:1-9— this particular story is under the law, in the old testament. The story took place approximately 100 years after the flood. The whole earth had one language and one speech– in which time God told Noah to take his family about the Earth– to spread out– and to re-populate.
As they journeyed from the east they found the land in Shinar– and dwelt there.
Humanity decided to build a great city so they could all congregate together. They also decided they wanted to build a massive tower that reached the heavens– to symbolize their power– to make a name for themselves, as if they were equal to God.
God was not pleased. He came down to see the city and tower that the men had built– He was displeased that this was the choice the men made– even though they knew what God’s instruction was.
So God scattered them among the Earth– confused their language, so that they would not be able to understand one another. The building of the city, ceased.
This is where the name Babel comes from– because it was there that the Lord confused the language of the people and then scattered them abroad.