A one-horse shay is a small, two-wheeled carriage pulled by one horse. The Wonderful One-Hoss Shay is a reference to Oliver Wendell Holmes' satirical poem The Deacon's Masterpiece. In this poem a Deacon builds a perfect one-hoss shay, built from all the best materials, and as such it has no failure points. It is, in fact, so perfect that it functions without error for 100 years, before suddenly disintegrating as the parts fail simultaneously.
This phrase is often used as a metaphor in technical fields, from structural engineering to biology, to refer to the counterfactual idea of the almost-perfect form; not something that will last in perfection forever, but something that has no obvious weak points. While this is something to strive for in the abstract, it is not a realistic goal.
In economics this is a more formal term, referring to a model of depreciation (also known as the light bulb model of depreciation), in which an item exhibits no reduction in value during its functional lifetime, instead losing all of its value at once when it breaks.