If you find your refinement suddenly disappearing, leaving a confused user (and some hedache for you), double check this property!
Its behavior is straightforward, and is exactly what the propperty name suggests.
You can define a threshold (unsigned integer value) that controls when the refiner is shown, based on the results that are returned by the search query.
If the occurrences of the underlying metadata property do not exceeed this threshold, the refiner simply disappears.
This may be appreciated: imagine a situation where you have defined, say, twenty refiners and you do not want to flood the page with every single kind of faceted filter. You need a way to prioritize this, and the Metadata Threshold property is what you are looking for.
On the opposite, you can of course eliminate it (just set the value to 1) if you need to keep a consistent layout across query executions.
If a property is there, and if you know what it does and how to prevent it, you gain flexibility!