Basically, it means that a photo that can tell you the feeling, the mood, the emotions, the story, the characters and etc etc..
If I'm not wrong since I'm also a new bie, I think it's voice down to composition of the photo, then follow by the rest like facial expression, the 'feel' in the eyes of the object or model, lighting effects, the backdrop, the crop, and others.
Great majority of the time, such 'story telling' are composed and 'dramatise' by the photographer and to use his skills, but sometime, it can be luck.