There are 3 things I look for in an image that make it work as visually exciting and prompt me to stop and shoot a picture. Light, Shapes and Composition. What firstly, to me, makes for an interesting visual image is the lighting conditions going on - the cast shadows and lit areas and their balance. Composition comes, and can be improved upon, afterwards by cropping - best to take more in the original image than you think you may want, then work on the crop. Shapes of cast shadows, pattern, negative and positive area balance are important for visual stimulus and impact.
Technically, depth of field, where you control sharpness and bluriness in forground/baclground, create visual depth. How the light and shadow areas are layered also help create depth. Having a focal point and the areas surrounding being allowed to visually recede, also create depth. This is something that also helps to create visual excitement.
It begins with the initial image taken with the camera, to the best of the photographer's ability and the camera's capabilites. Then, one can improve and manipulate the photo's composition and visual impact in order to achieve creating a visual impact on the viewer - whether it be to focus the vieweron a single lit flower and a couple leaves highlighted and brought forward by sitting against muted and shadowed deep areas around and behind, or the backlit glow of a butterfly wing - it's all about the visual impact of the final image. Photoshop, though I don't get carried away, and am still learning, is the tool that allows me to do effectively create a final image which gives me the same thrill I had upon viewing the subject of my image in real life.
So although some images from our walks are quick omg look at that shots to memoralize an amazing yet fleeting sight stumbled across like a hovering Kingfisher or bird feeding its young, other images are deliberate composed pieces of visual art. For me, it is most important to see as an artist and then to shoot like a photographer. I have a ways to go on the latter part :-)