For a photographer, the main advantage of mist is ‘atmospheric perspective’. A subject close to the camera will show normal contrast and colour saturation because the rays of light have not travelled through much of the mist. A subject further away will show lower contrast and saturation because more of the rays of light have been absorbed or diverted by the water particles in the air. Reduced contrast and saturation can turn subjects with strong colour to a uniform pale blue or grey.
Hills in a background can become barely discernable, adding a strong impression of depth to the image. The effect will be even more pronounced if you shoot in the direction of the sun, turning subjects closest to the camera into silhouettes.
You will often see this technique used with landscapes, especially with one hill after another receding into the distance, but almost any scene can be transformed by mist.