You may start your idea-generation process with a concept or with a character, or perhaps you have the theme or a scene in mind. It doesn’t matter where you start. You don’t have a story until you have characters colliding with a concept.
An example: I’m working on developing an idea for a fantasy novel, one whose time seems right, a story I want to tell, which I’m ready to tell. It started with a prince. I imagined him balancing on a parapet, a reckless move justified because he thinks he is guaranteed to be king, whether he wants to be or not, due to a prophesy spoken at his birth. It started with a peasant, who sneaks out of the house, quiet so as not to wake her controlling father, to honor the moon. She is destined to be a priestess, as her mother once was, though she knows nothing of that. I imagined the prince, disguising himself as a commoner, seeing the peasant girl, and wanting to help her. He does so, in disguise, and falls in love with her.
Perhaps this sounds like a story, or something that could be developed into one, but it’s not. This is merely two characters with a connection. This is not a concept.
I wondered what kind of world these characters would inhabit. It would be a magical world, but a world in conflict. I wanted this world to somehow connect with a novella-in-progress, so certain aspects of it were already set in my mind—though the novella isn’t published or even under consideration, so I can go back and change whatever I need to for the sake of consistency.
International war is bound to be an issue. But civil unrest is better fodder for the kind of story I want to tell. The prince, though highly privileged, is a good man who doesn’t love power. Though he takes his power for granted, he’s more concerned with justice than power. The peasant, though without even a semblance of power, is a strong-willed young woman dedicated to righteousness.
The theme is to be either the difference between righteousness and justice or the difference between submission and control. Perhaps both. Probably the intersection of both.
Right now the characters and their world are still somewhat separated. I haven’t integrated them yet. The theme in regards to the magic is the exploration of submitting to the magic, in order to restore balance, and the exploring of trying to control magic to achieve one’s end, and the consequences of both. The theme in regards to the characters is the exploration of righteousness versus justice; if one character is committed to righteousness and the other to justice, they’d frequently be allied, but not always.
The concept is the unifying factor, the influence that brings the characters, the world (i.e. setting), and the theme together. Their love, while more than a sub-plot, is not all of who they are, nor the greatest of their responsibilities. How can he do his duty, while pursuing his love for her? How can she do her duty, while pursuing her love for him? If they cannot find a way, which will they choose? Will they both make the same choice? Their duties are shaped by their world, which is much in need of them; but their love defies their roles, their differences, and their beliefs. This is the concept, though it’s not properly stated as such. (If it were, it would be a single, unifying question that the ending of the story would answer.)
Only when the characters collide with the concept is there a hearty enough, a unique enough, a true enough conflict to propel a story. Without conflict—purposeful conflict—there is no story.