All of these examples are by themselves good stories, but the idea behind them goes way beyond that.
One example from antiquity
"Oedipus The King" is considered a masterpiece of ancient Greek tragedy. In this tragedy, Oedipus has become the king of Thebes. He doesn't realize his actions are fulfilling a prophecy. The prophecy said that he would kill his father, King Laius, and marry his mother, Jocasta. This is more than just a good idea for a story. Yes, the misfortunes brought by the inevitable destiny is a topic of this tragedy, however, there is a deeper idea buried between the lines, especially the last line: "marry his mother".
Sigmund Freud, in his "The Interpretation of Dreams" says: "His destiny moves us only because it might have been ours — because the oracle laid the same curse upon us before our birth as upon him. It is the fate of all of us, perhaps, to direct our first sexual impulse towards our mother and our first hatred and our first murderous wish against our father. Our dreams convince us that this is so." This is the reason why Oedipus is so universal. It moves every man on the planet, appealing to what is hidden, willingly or not, knowingly or not, in our subconscious mind. Alarmingly, it is possible to find the same childhood attraction for our mothers -which could and could not be overcome in adult life- in artistic and literary expressions from several cultures and geographies around the planet. The play is so powerful that several movies have been created based on it. Pier Paolo Pasolini directed an adaptation of the play in "Edipo Re". "Funeral Parade of Roses" is a Toshio Matsumoto's version of the play. Gabriel García Márquez adapted Oedipus to his local reality in Edipo Alcalde.

An overlooked novel
Erich Maria Remarque, the author of "All Quiet on the Western Front", also wrote, "Heaven Has No Favorites" (1961). The story is about an automobile racer who meets a lady in a Swiss sanatorium. She is ill with tuberculosis. They leave the sanatorium and have fun together for a brief period of time. They both return to their separate lives. Shortly after that, he dies in a race. After her return to the sanatorium, she also dies. Not an exciting idea, is it? You may think: "This is not a very good idea for a novel." Things happen, yes, but it seems that something is missing. Then why is this novel so engaging and why I am bringing it up? Because the missing message is between the lines again and it is as powerful as an Indiana Jones adventure; certainly, an unforgettable book.
What the racer and the sick woman have in common is their limited lifetime. They know they are going to die. It's inevitable. Sooner or later, death will come to take them as it will come to take us all. They do not have a lot of time to live their short lives. Most of their lives they have been living an announced death, like all of us. The unplanned encounter brings them the illusion of love and during their short time together they try to enjoy life to its fullness traveling through Europe. He even imagines them living together. But at the height of their happiness, she returns to her reality. She doesn't want him to become a widower immediately after their marriage. So, they break up and ultimately died apart.
Human beings are the only animals aware of their own death, supposedly. Very early we begin to hear about it. We do not understand its meaning even in our adult life. Amid children's games and fables, we start to be certain about one thing, though: Death is inevitable. It makes our lives seem shorter than it is. It leaves us with the feeling that we do not have enough time to live our lives. We go through life waiting for our death, fearing it will show up at the least expected moment. Love can take us momentarily out of these disturbing thoughts... for a short time. Love can lift us up and make us forget the inevitability. Death is such a primal fear that it can even obscure the happiness we have achieved with so much difficulty.
That is the actual idea behind an apparently simple story. It goes again way beyond the story itself.
Gaiman's novel
Coraline is a contemporary well-known story. They even made a movie out of it. The way Neil Gaiman explains the idea beyond the story is very interesting. He maintains that he tells lies because fairy tales aren´t true. Telling lies is a way to tell children that there may be bad people out there, people who can hurt them. He thinks that these lies are important not because they talk about dragons that do not exist. But rather the lies can teach us that the dragons can be defeated. These dragons represent hard times, fears, limitations, obstacles, and any sort of threat that is making us miserable. This is the idea beyond the story in Coraline and that is why the story is so engaging. This is another universal human experience, always present throughout our lives and the lives of all of us. He explains this further: ..."some things, when you get really specific apply to so many of us."
Time to get personal
I´m not going to tell about the idea beyond the story in the novel I am currently writing. Instead, I am going to talk about a perfect example from my writing. In my fantasy novel, The Bottom of the Spiral, there is a chapter for which I wanted something equally ubiquitous in the subconscious mind of human beings and still as original as possible. From the reading of Joseph Campbell´s The Hero with a Thousand Faces, I was certain that the Minotaur represents any interior threat that stops us from being the one we want to be or the one the destiny expects us to be. It is for us to go deep inside our mind to defeat this monster, and come out victorious; knowing what to do to give meaning to our life, to become what we seek. The Minotaur represents any interior obstacle. The way I found to create my own version of this monster was to be very specific. My monster is called Osterácodo. He represents the behavioral patterns that we all follow and of which we are unaware. This is the monster that makes people find the next abusive partner over and over throughout their existence, wondering all along why is it that only abusive people come to their life? They do not see why. They do not recognize the ones capable of hurting them. They cannot distinguish abusive people from the loving ones. They do not recognize a previous identical situation until it is too late. This is why my Osterácodo lives in a labyrinth constructed of ceramic. The floor cannot retain the desperate monster's footprints, and the walls do not absorb any passing traces of odors. Consequently, the Osterácodo cannot recognize that he has been there already, in the same situation, with the same kind of lover. Frustrated, the unhappy monster wanders around his labyrinth looking for clues, for patterns, for traces, and for vestiges of knowledge about himself so he can free himself from his inner hell.
For you to think.

These examples show clearly what I am talking about when it comes to "the idea beyond the story." I would like you to think of something similar for your novel. It should be something that is not a personal experience. On the contrary, it should be something common to all human beings. As I said, previously, this is not necessary for writing a novel, but it makes it much better!!