It is all about communication.
Photography is a visual language that requires the right vocabulary and grammar to communicate effectively. Looking at an image it should be apparent to me what it is about. Or it should be intriguing and thereby provide an invitation for further 'reading' of its story. If the image cannot connect to me as the viewer, it fails its purpose.
Similar to good prose or poetry, the essence of a good image comes from the multitude of decisions that the author has made during its creation. Mostly, it is a process of elimination, by subtracting all the non-essential information from the frame, thus reaching a clear visual expression as the end result.
As personality is an important part of the decision making process, a good photograph often conveys a personal aspect of the photographer.
Great images connect with us in an instant, they deliver their message and leave us emotionally touched, educated, inspired or otherwise impacted, with the visual imprint often lasting for a lifetime.
(A piece that I wrote a few years ago and just rediscovered.)