Every child has a rebellious moment where they want to run away. Maybe it's just that adventurous streak every child has coming out to show it's face. Maybe it's because you're mad at your mother or father because they want you to do something you have no interest in. No matter the reason, children tend to always toy with the notion of running away.
My big run away moment when I was a child was when I decided to 'run away' and walked to the end of my street. By that point (the walk to the end of my street took me about a minute as a grown up to walk) I figured my mother was worried sick and I had been gone for hours so I turned around and walked home.
The little bunny in this story by Margaret Wise Brown has that adventurous streak and decides he wants to run away. With the imagination that only children, artists, and authors can have the bunny describes all of the things he could be to get away from his mother and in turn his mother points out how no matter what, she'll be able to find him and love him.
Eventually he figures he won't go to all the extremes of running away but remain where he's at.
Some people proclaim that this story is creepy, that it displays a way a mother shouldn't behave. "The little bunny wants space! He just needs some time to himself!" Really? Assuming the bunny is a child I'm sure he's just trying to be rebellious or annoyed at something very silly. I feel the true point of the story is that a mother, no matter what, will love you and be there for you. Whether you are a boat sailing away or a rock on a mountain your mother is always there.