Cooper's Law applies not only to machines, per se, but to any unusual or unfamiliar object in a story that would attract the attention of the reader. This is as opposed to familiar objects that are introduced to provide a setting or create atmosphere.
The meaning of Cooper's Law is that in a well written story, any gadget or implement that becomes an essential part of the narrative, belongs in the story because it serves the particular purpose of excusing unnatural or exagerated behavior by the characters, which the reader would otherwise not accept.
Possibly the first and clearest application in science fiction would be the drug used by Dr. Jeckle in Robert Lewis Stevenson's story The Strange Case of Dr. Jekyll and Mr. Hyde. Dr. Jekyll's drug serves the function of a Cooper Law "machine" in that the drug excuses the otherwise unbelievable behavior by the character who has imbibed it.
The practical use of Cooper's Law is in editing stories: If a writer has even mentioned an object that does not fulfill Cooper's Law, then the story could probably be improved by removing it.In a treasure story, the object that amplifies normal behavior is the treasure being sought by the characters.
Cooper's Law is closely related to Langford's application of Clarke's Third Law to science fiction: "Any sufficiently advanced technology is indistinguishable from a completely ad-hoc plot device."
Another closely related rule of fiction is the depricated Deus ex machina, where a machine, or a magical character (such as a god) is brought into the story at the last minute to quickly resolve a tangled plot.
The idea bears some superficial similarity to Kurt Vonnegut's idea of the wampeter. However a wampeter if used as a fictional device, would be a thing or a place that serves as a symbol or a talisman to represtent an arbitrary collection of charcters.