Genesis 11:1-9 -- Tower of Babel

Genesis 11:1 At one time the whole earth had the same language and vocabulary. 2 As people migrated from the east, they found a valley in the land of Shinar and settled there. 3 They said to each other, “Come, let us make oven-fired bricks.” They used brick for stone and asphalt for mortar. 4 And they said, “Come, let us build ourselves a city and a tower with its top in the sky. Let us make a name for ourselves; otherwise, we will be scattered over the face of the whole earth.”
5 Then the Lord came down to look over the city and the tower that the men were building.6 The Lord said, “If they have begun to do this as one people all having the same language, then nothing they plan to do will be impossible for them. 7 Come, let Us go down there and confuse their language so that they will not understand one another’s speech.” 8 So from there the Lord scattered them over the face of the whole earth, and they stopped building the city. 9 Therefore its name is called Babylon, for there the Lord confused the language of the whole earth, and from there the Lord scattered them over the face of the whole earth.

The people of earth wanted to be recognized.  They wanted power here on earth.  They were to demonstrate the power by building a great city with a tower that reached into the heavens.  The Lord disapproved and as a consequence, so they could not do it again, he confused their language and  scattered them.  Now the people could no longer understand each other and  communicate about how to build the city.

Now one may stop and say, but didn't they say in chapter 10 that each people had their own language and were already scattered around the earth?  Yes, in chapter 10 they do say that, but keep in mind Genesis is not linear.  Remember how God described the creation of the world, but then later goes into detail about how he formed Adam and Eve?   That is what is happening here.  In chapter 10, all the families were described and it was told where they went and that they each had their own language.  In the story of Babel, you are seeing a more detailed account of how they became spread out and how they each got their own language.