It's hard to really describe what makes one photograph awesome and another one bad in such a way that the meanings of the words that I presently use to represent abstract ideas in my brain map to the same mysteriously indescribable abstract ideas in your brain. So it's how I view the art right now, but it's probably verifiably wrong in all sorts of ways.
The most important thing is the Presence of the photographer. Sometimes this means that the photographer hiked all of the way up a snowy mountain with snowshoes and a camera and caught the perfect view.
Sometimes Presence is about Personality. Working with models has taught me that my disposition and the way I talk to the models causes them to unconsciously do things. People are different. Some models I connect with well, others I don't.
Sometimes Presence is about Persistence. I went up to see Mount Rainier the other day and it was fogged in. I took photos anyway, found some stuff worth photographing. Some photographers hit the same spot over and over again, always finding new things. Other photographers are constantly exploring to find new things.
Presence is also about Poignancy. Catching a set of dishes the night before they were torn down is different than other nights. Perhaps it's me telling you that I caught the observatory before it died... or perhaps it's that I somehow communicated it.
The controversial work Piss Christ that I remember from the culture wars of the 80s wasn't poignant because of the piss, it was poignant because it was so outlandishly outr? that everybody had to talk about it. I can't re-create something like it with my own urine and have it make any sort of effect.
Poignancy is about Preservation. Pictures taken on Brownie cameras in the early 1900s were not taken with the intent of art, but now they are incredibly poignant because most of them haven't survived.
Presence and Poignancy is that unconscious thing that makes a poorly executed unskilled photo look cool anyway. It's also entirely about Probability. Catching your neighbor in a compromising position is one thing. Catching a celebrity in a compromising position is another. Carrying your camera with you helps. Much can be compensated for by taking a lot of pictures.
Next, you have skill. Skill is understanding colors and composition and lighting and structure. It's about pointing the camera in the right direction. It's about knowing how to keep a cat in the right position, a kid smiling, and a model posing. It's about knowing how to take a picture with a ridiculously slow shutter and have it come out OK.
I don't like seeing skill solely as the things that you are taught. Really, it doesn't matter. Ansel Adams always draws a comparison between photography and music. I know plenty of musicians with no formal training but who have a ferociously good ear. I know plenty of musicians with a great formal understanding of notation and harmony who are unable to produce music that people really like to listen to.
Where the presence and skill hit the pavement is the lens. Recent history has greatly obscured this. A long time ago, the camera was little more than a light-tight box and so the image quality of the body was mostly to do with the selection of film. Digital cameras mean that your image quality is driven by the camera body instead of the film.
Furthermore, modern computer power lets designers algorithmically model all of the features and properties of lenses and try out a wide variety of designs. Modern machinery allows you to create lenses with complex aspheric designs with complex coatings and then assemble them into a design that can be built cheaply with the required tolerances. And tiny sensors make it easy to make lenses.
Thus, your lens still really matters. It's just that even cheap kit lenses are actually pretty good. Even the camera+body combination in your iPhone is actually pretty good.
You can't capture birds in the distance with an iPhone camera. The lens is not narrow enough. Similarly, there are pictures that require the photographer to capture them with a wide angle lens.
On the other hand, I know some people with animal magnetism in ways that I don't have and they can get really close to skittish birds in ways that I can't. And wide angle lenses take some skill to get right. So skill is more important, but you can put the widest wide lens and the narrowest telephoto on any body in the system.
It's even about the tasteful use of a bad toy camera lens or a pinhole non-lens.
Finally, the rest of the equipment. Again, because of recent advances, you can get a mirrorless body or a dSLR for not a whole lot of money with a good-enough kit lens. You can build a studio with a high ISO and some regular lights. You can use a rock or two as a ersatz tripod. So it doesn't matter as much as it used to.
And sometimes the rest of the equipment drives the more important things. When you buy a SLR or interchangeable mirrorless camera body, you are locking yourself mostly into one system of lenses. There are adapters, but adapters come with consequences. Given that the lens is often times more important than the body, you can't just get whatever happens to be on sale at the moment.
Part of why I ended up going for my Olympus is because I liked the Micro 4/3rds lenses better. Part of why Fuji has done well with their mirrorless camera system is because Fuji has also shipped their camera with a bunch of really nice prime lenses. Micro 4/3rds has the best set of pancake lenses. Fuji has a great set of prime lenses with some special features. Canon's SLR mount has traditionally had the best telephoto lenses, Nikon traditionally has had the best wide angle lenses.