There is no standard or universal definition of this genre. In fact, it is not easy to create a clear definition of the abstract concept. But, it will be easier to determine what goes into the limits of this type of photography. Namely: can not display clearly, and convey ideas through shapes, colors, and curves.
This definition then gives an important point. Because of the details of an object formed of shape, color, and curvature, the brain is logically something abstract through instinct. In essence, abstract photography communicates to people who see it-generally-through emotions. This certainly benefits the photographer because the human emotional system is stronger than the logic system.
If made well, an abstract photo can be very much aligned with the perception, mental, and human emotional system. The end result can be something very powerful. Important for abstract notes does not always mean "unrecognizable". It's true, on some abstract photos, one can not hold back what the real thing is. But, this turned out to be one type of abstract photo.