Look at the composition. If there are elements that lead the eye in a certain way and seem to be related to each other, it might be a good story - telling picture. For example, in a photo of a fisherman on a boat, if the fishing rod is extended towards the sea where there are some fish jumping, it creates a narrative. Also, color can play a role. A picture with a dominant color that sets the mood, like a grey - toned photo of an old, abandoned building can tell a story of decay.
One way to identify such pictures is to consider the expressions of the subjects. In a portrait, if the person has a sad look and there are elements in the background that seem to add to that mood, like a wilted flower, it tells a story. Another aspect is the use of light and shadow. A picture where a single beam of light shines on a lonely figure in a dark alley can create a sense of mystery and tell a story. And if there is a sequence of pictures, like in a photo - essay, the flow from one image to the next can help identify those that tell a story well.