McGrew is a pretty typical kid, so we're guessing he doesn't have much power to change the real world. He probably can't even decide his own bedtime. As a child, McGrew isn't the one in charge, so he has to follow the ideas and thoughts of others. Or does he? In lieu of a magic lamp, McGrew will change all that with his imagination.
First, he changes himself by taking on the clothes and identity of the zookeeper (see the illustration attached to stanza 3). Next up, he changes the zoo by removing the animals he finds dull and rote. Which, by the way, are lions and tigers. Go figure. Finally, he travels the world searching for all manner of exotic, weird, and oddball beasts to occupy his zoo.
As we are reminded several times throughout the book, this zoo belongs to McGrew. More than anything else, McGrew's imagination desires to change his situation from a child who has no power to the man in charge of everything.
And it makes sense. Children don't have a lot of control over their lives, and the book really taps into this longing. After all, a child completely controls his or her own imagination (don't we know it), so they have the power to change anything within their imagined world. And we mean anything. In a way, imagination is the only place in our lives where any of us have complete and total control.