Storytelling in graphic design is a way of creating emotions, imagery and understanding of the visual interaction between elements. It is uniquely human and most compelling. In graphic design the elements need not be obvious but rather represented in an abstract manner. For instance, the flow of water can suggest movement in time of civil rights struggles, and water flowing over an edge can be a victory or struggles overcome. Another example is that most graphic designers in Los Angeles know the top of a mountain represents success and is widely used in business graphics and photos.
Freelance graphic designers can also use storytelling in that a design can have a setting, mood, characters, plot (purpose or goal), and movement (flow of elements). Much like a story, the invisibility of the designer fades as the audience is engaged in the visuals.
Use storytelling in your graphic designs to engage audiences, evoke emotions and provide a rich context. It can be quite powerful, as when a viewer recalls the design's story in a personal way it becomes a part of her.