Storytelling is the conveying of events in words, sounds or images.
Stories have been shared by human beings for tens of hundreds of years as a means of recording and representing the world and the purposes of:
Entertainment
education
cultural preservation
instilling moral values
Crucial elements of stories and storytelling include:
Plot - cause and effect process that develops, ordering of events.
characters
narrative - all the means to communicate with plot and story.
point of view
The term storytelling is sued in a narrow sense to refer specifically to oral storytelling and in a looser sense to refer to narrative technique in other media.
The 'story' part is everything to do with it. It is the chronological world of the film.
Visual storytelling applies to film and a host of other media. Sometimes it carries with it a prescriptive edge: in a pictorial medium, you should tell your stories visually - rather than, for example, through lengthy dialogue. Show, do not tell in other words to try and explain it. As a concept visual storytelling refers to the way that producers of moving image products convey the meaning of action and events through images without recourse to the written or spoken world.
This is achieved through two techniques:
the choice of shots
the way those shots are edited together
In film, it needs concepts, music, sound and much of the time a modicum of dialogue to work most fully. BUT given the power of the image, a director who invests in purely visual passages first and then considers how his/hers images might be reinforced by other inputs, gains huge dividends in the long run.