"Premise" comes from two Latin words, meaning to put before. The premise is the foundation of your story—that single core statement, says James N. Frey, "of what happens to the characters as a result of the actions of a story."
For instance, the premise of The Three Little Pigs is "Foolishness leads to death, and wisdom leads to happiness." (It's not three little pigs get scared by a wolf and make bad building decisions.) Every story has one premise. Only one. This premise is the underlying idea of your story—the foundation that supports your entire plot.
If you can establish what your premise is at the beginning of your project, you will have an easier time writing your story. That's because the fundamental concept you create in advance will drive the actions of your characters.
Once you establish your premise, you then set out to create a plot that proves it. The discipline of expressing your driving idea will prevent you from wandering too far from your original concept and keep your plot on a steady path from the beginning through the middle to the end. It will also help you craft a story that works.
A story premise can usually be stated in one sentence, and--because of the universal truths premises tend to express—a premise statement is often a familiar expression or cliché. "Honesty is the best policy," "be careful what you wish for," "what goes around, comes around," even "love means never having to say you're sorry" are all valid premise statements. Think about the story ideas you're working on and try to craft a premise statement for each of them.
To learn more about crafting stories for children, check out the Fundamentals Of Writing For Children Workshop.