The Tower of Babel was an attempt by the post-Deluge peoples – all of whom spoke a common language – to build a structure upon the plain of Shinar which would reach to Heaven. God took offense to this, and went down from Heaven to prevent the project from succeeding. Having a keen understanding of the importance of good communication, God’s method for disrupting the project was the change everyone’s language. He created an un-recorded number of languages that day, sundering families and friendships, and all to prevent people from reaching Heaven physically.
The traditional religious interpretation of this is that it is a warning against pride. However, God’s words, as recorded in the Book of Genesis, make it fairly clear that, not unlike with that unfortunate business with the snake and the fruit, God was once again acting from fear that mere humans could dethrone Him by equalling him in power.