In Picture Books, the text and illustrations will have varying degrees of responsibility.
Wordless Picture Books rely entirely on the illustrations to carry the story.
Other books, like BJ Novak’s The Book With No Pictures, rely entirely on text.
Most picture books marry the two extremes and use both vehicles to appeal to all the senses of the adult and child audiences.
Often, a writer creates a story with text and then publishers find an illustrator who can tell the same story with pictures.
“I don't think of myself as an illustrator. I think of myself as a cartoonist. I write the story with pictures - I don't illustrate the story with the pictures.” -Chris Ware
But the role of the illustrator is not simply to elaborate.
“When you make illustrations, you're supposed to have a subtext; you're not just communicating words - you're actually adding another story altogether.” -Peggy Rachmaninov
Storytelling is multidisciplinary.
Illustration and text are only two vehicles used to tell a story. There is also:
Exploring different vehicles to tell your story may help you flesh it out completely, or you may land on a vehicle that suits the story you are trying to tell better than others.