In England, these were called laws of primogeniture. The younger sons usually pursued a new life in the new world. A good example of this was John Smith who was famous for Jamestown. Interestingly, these unfair laws led to the formation of many colonies in the new world. This was primarily in the 1600s and 1700s.

I'm not quite sure about the Medieval era, however I can probably assume that the younger sons would become merchants or join the army.