This is a camouflaged camera, or spy camera, that could be hidden under a vest when the vest was a standard part of a man's clothes.
The camera was built by the American R.D. Gray, and manufacturing rights were later sold to the Stirn brothers. Rudolf Stirn produced the camera in Berlin, and it became a great success. From October 1886 until 1890 18,000 units were made and sold.
The camera contains a round glass plate (a dry plate) with room for six round exposures, each with a diameter of 4.5 cm.
The camera body itself is flat and can be hidden under the vest. The lens and the film advance stick out from button holes, so you could photograph undisturbed whatever was around you.