We could say that a good photograph is one that is correctly exposed and properly composed or an image that attract and holds our attention by being emotionally compelling. Certainly, this definition will serve well in teaching the fundamentals of photography.
At the same time, I think there is a lot more to consider. For Bernice Abbott a good photograph must be "utterly honest and direct." However, for me, a photograph is "good" not only when it honest, but when it is memorable. Although a concrete reflection of reality, a memorable picture illuminates and edifies. The picture, Halla Beloff reminds us, is a way of making sense of our own history. I think this is why there is such a fascination with "selfies." We are constantly constructing new narratives for ourselves in the virtual space of Facebook or Twitter. The "good" photograph lies on the surface of a deeper more complex reality; a form of narrative intent, which sets out to touch the soul and make us reflect on what it means to be human. it is, as Lady Elizabeth Eastlake observed in the 19th century, "profoundly interwoven with the deep things of nature." I am afraid of what we understand as the aesthetics of the frame is under attack by the millions of us that toss images of ourselves onto a screen like Jackson Pollock tossed paint. However, I think Pollock had a bigger vision.
It seems that for many people the only objective in taking pictures today is in getting noticed by others. Images on Facebook tend to be unapologetic in terms of applying any true set of universal principles such as beauty.
For me, there is a great deal of ritual in making pictures. There is the expectation of putting myself in a space that opens me up to seeing the world in a new way. Any image that enters our consciousness is a gift and we have an obligation to do our best to capture the experience in only a way we can. Ultimately, the "good picture" is something that come's first from the mind's eye and is then transformed into a new reality for others to remember and think about.
What makes a picture memorable? First, the image must be technically correct and well composed. However, it is in the relationship we have with the content of the image that makes it worth remembering.