Cucumber slicer / vegetable slicer from c. 1920. EvaK / Wikimedia / 2006 / CC0 1.0
Cucumber slicers allow a cook to create very thin, uniform slices of cucumber to be used for sandwiches, salads or garnish. The name is a bit of a misnomer, as the devices are typically used for other similar firm types of produce such as carrots, zucchini, etc.
There are two different types of cucumber slicers.
One is a round device turned by crank. You clamp it to a table and press the cucumber through with a pusher. Original ones were made of cast iron.
Another type is a flat, rectangular surface that you drag the cucumber over. It looks like the bottom of a wood plane, or a mini-mandoline, in that it has a metal blade on an angle. Some have two blades on them. Antique ones were made of wood; more modern ones are made of metal or plastic. Metal ones may have the blade built into them, rising out of the metal. Older ones had adjustable-angle blades.
Substitutes
Sources
Erlanger, Steven. Unkindest cut over a humble cucumber slicer. New York, NY: The New York Times. 5 October 2002.