To become is to evolve, change into, or emerge as something. A fertilized egg will hatch and the tiny chick will become a full-grown chicken.
When you become angrier and angrier watching the TV news, you begin to feel a certain way. Likewise, when Pinocchio the wooden puppet becomes a real boy in the fairy tale, he changes from toy to human. The word become can also mean "learn how to be" or "be qualified for," as when you dream that some day you'll become an astronaut. The Old English becuman has these meanings, and also "meet with" or "arrive."