Its an Air-Mite press, they may not make them anymore like that one. I can't tell what model it is, I'm guessing AP4, thats a 2" cylinder.
The company name is under new ownership, but the new fellow is supporting the old stuff. There is a company website. They come in various strokes and sizes, that looks totally stripped. Probably a leaker, they require regular maintenance.
Its used for punching holes, stamping circuit boards, crimping, forming metal with a punch die etc. Most are set up using a foot switch, I've seen electric controls and manual pneumatic hand switches. Think of it as an air powered arbor press. They are useful and have many, many applications.
Also: you can find the control switches used on eBay. You need to determine the model, is it a dual action or single? They can be converted back and forth, but the control air switch need to match the press action. The press can be run directly off a normal air hose, no valves needed unless its dual action and you want to speed up the strokes. Thats not needed unless your in a production setting with a quick repeating process and a good operator. I've only seen them manually operated, there might be auto feeds out there.
If you want auto, then I would go with an electric driven press. I have an old 2 1/2 ton 110 volt press, I think its called an Alva or something. I've been trying to find a purpose for it, it came with an auto feed roller and it does run. Its so small, probably stamped out something like electrical terminals. It was too cool to let it be scrapped, got it for free. I'm a sucker for free "get it out of my way" deals.