Sorry, cant see the pics (webfilter). I see you are in Philly. Those basement walls often have what the locals call parging on them. Its a masonry coating that flakes off over time if you have water issues.
Of course I'm guessing here but when u ask if its plaster thats what I think of.
Your first step is to deal with water OUTSIDE. make sure the ground slopes away from the house, the gutters are not overflowing and downspouts extend away from the house by 6 feet. Doing those things will likely dry out the basement. Then the old parging can be scraped off and a mason can re-parge.
And to add to that I'd bet it never got water proofed on the outside before back filling.
You may even need to go so far as to add a french drain and also waterproof on the outside if you really want to perminitly fix this.
Had the same problem in my basement. Handyguys is right on the money. That is parging and it is flaking off due to a water issue. I solved my problem simply by adding top soil around my foundation which established a positive grade for proper water run off. My downspouts were fine. I just needed to get rid of the flat areas (and negative grade) next to the foundation. If this measure doesn't work you will need to take more aggressive (and costly) steps such as a french drain like previously suggested.