What do you want to convey in your story? I'm not talking about preaching or moralizing, but the concept you want a reader to take away from your story. The theme.
Theme might be called an underlying truth. A foundation for the story that will help guide the story. A focus or center. It's not plot. It's not necessarily the subject. It's might be described as something important that the writer believes applies to the subject.
For example, in the Harry Potter stories, the theme is "good conquers evil." The theme in the Twilight series might be "true love overcomes all." These concepts are not stated in so many words. The writer shows the theme instead of telling it.
In a novel there can be multiple themes. i.e. Harry Potter books: "loyalty to friends," "hard work" and "perseverance." The Twilight books: "protect your family" and "don't give up on getting what you want."
Often authors have a common underlying theme for their non series books or book series that feature different main characters. One adult author I read comes to mind: LE Modesitt Junior's books often express the theme of "hard work;" so much so that his characters make me feel lazy. Yet, he's not preaching at me. Instead his characters believe in hard work and follow through and I become impressed with what they do as I read. Modesitt must also believe in hard work--just look at his number of published novels.
I recently read a blog entry on theme that makes a lot of sense. Novelist Larry Brooks. says theme helps a book be memorable. He recommends including your theme in your "What's your book about?" answer. Read more at http://menwithpens.ca/fiction-writing-story-theme.
Laura Elvin refers to it as the "why of the story" in this article on theme in short stories.
Now what about premise?
Some writers use the terms theme and premise interchangeably. Rightly or wrongly, I view theme as general and premise more specific. So back to Harry Potter: "a young good wizard will conquer the evil old wizard." A premise for the Twilight series might be "if her love is strong enough, a girl can even win the vampire she loves." It's the kernel of the story. Premise might also be described as the situation or the central idea of the story.
Jeanne Vincent has an interesting article on the difference between theme and premise. Alexandra Sokoloff talks about the premise being the pitch for the story. I like her approach. Read it here: http://thedarksalon.blogspot.com/2008/05/whats-your-premise.html
However, whatever you call them, these concepts are necessary for a compelling story. You may use them unconsciously as you write or you may have to plan.
Thinking about these again makes me realize I need to make sure I know what the themes are for my works in progress. I believe knowing will help me focus my stories and in the end result in a better project.