There's more than one way in which a photograph can be influential, and four out of the first five (which, as a non Facebook user is all I can see) are probably influential in the sense of influencing public opinion. I don't know about the first, as that is blacked out for me; if it's the one I'm thinking of, I think it's legally a paedophilic image in the UK. The skyscraper lunchtime is the only one that isn't, and that's going to provide my jumping off point.
There's a book called "A Staggering Revolution" subtitled " a cultural history of photography in the 1930s" or something similar. I've read it. It's solely concerned with American (and North American at that) photography, and is written by a sociologist not an artist, art historian or photographer. In passing, for those who read such things - notice how few books on the philosophy of photography (or "critical theory") are written by photographers. Some of the most influential ones have been written by people who, in my opinion, don't understand the photographic medium.
Back to the Staggering Revolution. It covers a lot of ground, but the two major points I want to look at are that the author describes the 1930s as the most creative period of photography; he also (probably unwittingly) also states that at this period photography as an artistic medium was still in its infancy; unlike more established art forms, there was no fixed network of arbiters of what was good or bad - no major museums, curators, etc. etc. Consequently (my reading) photography could be experimental. There were many different forms photography could take - portraiture, natural history, fine art etc. and the poor relation (not regarded by some as being in the least artistic in either intent or execution) was documentary. Photographs like the skyscraper girder one changed that. As did the major exhibitions of the FSA and, post war, the installation of Edward Steichen at MOMA. Documentary now became the only game in town, and professional arbiters came to decide what was good, what was bad, and what was shown. Photography in the 1930s, said our sociologist author, was democratic. Afterwards, sez me, it was autocratic.
That's why there's a need now to provide lengthy statements, because now photography is another way of writing sociology. Look at recent themes and movements and they are almost all sociological and from a left wing perspective.
Returning to "influential" there have been many photographs in earlier times that were influential is creating movements in photography, or changing the way photographers looked at the world. Unless these were covered in the parts I can't see, the article is rather limited in scope.
There should be something (in the picture in this case) that tells you something, a story if you like.
This seems to me to be accepting the idea that photographs are documentary in nature, and must provide information. I regard this as too narrow a view.
In passing, there's no indication that I could see from url or the site name that it's a Facebook page; but attempting to move down produces the familiar command to sign in or sign up if you want to continue.