Okay, let's imagine you're playing with toy animals in a big field. There are some animals that like to live in the trees and some that like to live on the ground.
Now, imagine you start to clear some of the trees out of the field so there is more open space. You might notice that the animals who like to live on the ground start to do better because they have more space to move around and find food.
This is kind of like what scientists think happened a long time ago. They think that the world used to have a lot more trees and forests, but then things started to change. Maybe there was a lot of dry weather or maybe people started using fire more. Whatever the reason, more and more trees started to disappear and big open grassy fields started to take their place.
Some animals who used to live in the forests didn't do well in this new environment, but other animals who liked the open spaces started to thrive. This is the savannah hypothesis - the idea that grassy savannahs spread across the world and changed which animals were most successful in different places.