Your story concept can emphasize characters , plot, or theme. Of the three, characters and plot are by far the most common. And to keep our story going, you need to develop plot and/or character obstacles, complexities, and backstory.
An obstacle hinders your plot or character (not that the two should truly be separated but authors tend to emphasize one over the other). You will need a character and/or plot that is attracts obstacles like windows attract birds. You need obstacles that will slam into the character/plot so hard that one or the other will break. One way to do this is to adjust your character/plot so that it encounters people with conflicting viewpoints and goals. A second way is through rich settings that hinder or challenge the character’s personal journey or provide physical obstacles to reaching the goal. A third (almost fundamental) way is to develop characters who act as rivals, opponents, and deceivers.
A complexity is a detail or cluster of details or hints that you can later explore either because you are stuck or because you want to enrich your story. This could be a character’s necklace or a beggar in the street who your character helps, avoids, or abuses. It could be ruins in an ancient forest or a scar. Any of these details can be brought back later and explored more in depth. They can become the source of new conflicts, goals, or revelations. Explaining details is also an excellent way to get unstuck.
A particular type of plot and character complexity is backstory. Backstory is the past events before your story started – either in the plot or in a character’s life. Backstory helps you better understand character and plot because it explains why people and events now are what they are. Backstory can explain character motives and what plot paths are opened or closed. Relationships between groups (political, for instance) and individuals (animosity, perhaps) all have backstory. But so does the land, the nation, and cultures that your plot and character lives among. This is why so many writers advocate character and setting sketches and why writers of certain genres spend so much time on world-building. What happened before shapes and generates current (and future) characters and plots.