My screen/storm door started slamming a lot when the weather got cold. I adjusted the screw and it got better for a bit, but then would close really slowly, or start slamming again. I replaced it, and being curious, cut the old one open to see how it worked. (Google searches turned up nothing, so I'm posting here.)
The first lesson is that it was all air operated--there's no fluid like in a car's shock absorber. The bulk of the thing is a cylinder and a piston and the screw adjusts how quickly the air is released as the piston compresses air in the cylinder, thus determining how quickly the door closes. The cylinder contains a big spring that gets compressed when the door is opened and pushes it closed when you let go. The piston part has a rubber O-ring around it as a seal.
The O-ring rests in a groove that is a bit wider than the rubber ring, so that the ring can slide a bit. When the door is opened the O-ring slides, letting air go past the piston through four passages in the piston (see photo) and the door opens easily. When the door closes, the O-ring slides to cover up the passages and the piston compresses the air in the cylinder. It works similar to a bicycle tire pump, where the piston compresses air in one direction and then pulls back easily in the other direction. These parts were lubricated with grease. I suspect this is where the door closer was giving me trouble--the O-ring may have been failing to seal properly when the rubber or grease was affected by cold temperature.
It was not obvious how the adjustment screw works. A close look showed that the threads in the female part had 2 or 3 grooves cut into them along their length, creating small passages for the air. When the screw is turned outward, these passages get shorter, the air can get out of the cylinder faster, and the door will close more quickly. I suppose if some debris was getting into this area the door could operate erratically.
Inside the large spring, which was about 1 inch in diameter, was the piston rod which eventually connects to the door frame. Sliding along that rod was another spring, about 1/2 inch in diameter and 3 or 4 inches long, and very stiff because it was made of heavier wire. (See first photo--look carefully.) This appears to have two functions: when the door approaches the maximum-open position, this short spring starts getting compressed to reduce any shock as the door reaches its maximum open position (possibly when caught by the wind); and second, when you let go of the door from the fully-open position, the short spring will give a push to start the door closing quickly.
Finally, there is a very subtle thing I almost missed. When the piston reaches the almost-closed position, about 3/4 inch from the end of its travel, it reaches two small depressions in the cylinder wall. (They are visible, as bumps, if you look carefully at the outside of the cylinder. See orange arrow in the first photo above.) When the piston gets there, some of the compressed air will leak past these depressions and the door will suddenly close a little faster. The end result is that the door accelerates a bit just before finally closing so that there is enough force to get the latch to work. I have seen this advertised as "two phase" closing.