Typically, the new class will be a more specialized version of the existing class.
For example, you might define a class named Animals.
Then you might extend that class into two new classes named Carnivores and Herbivores.
They would represent more specific types of animals.
Then you might extend the Carnivores class into classes named Dog, Wolf, Lion, etc., to represent even more specialized types of animals.
You might extend the Herbivores class into new classes with names like Cow, Sheep, Horse, etc.
Typically, the new classes would add methods and variables that are more appropriate for an object of the more specialized class.