The minimum efficient scale is the amount of output that is most efficient for a company to produce. This is usually not a single number of output but is more typically a range of outputs.
Typically, there are economies of scale related to businesses. The larger a business is, up to a point, the more efficiently it can produce its outputs. But, after a certain point, this stops being true. It is often the case that firms will actually start to become less efficient as they grow bigger. This is where the minimum efficient scale comes into play. There should be a “sweet spot” in which a firm has already benefitted from all the possible economies of scale, but at which it has not yet gotten so big that it is experiencing diseconomies of scale. This is the minimum efficient scale.
The minimum efficient scale will be different for different industries just because some industries have more need for size. For example, a cell phone company needs to be really large so that it can have cell towers all over the place. By contrast, a firm that provides delivery services for people in a small town will not need to be very big at all. Minimum efficient scale is a level of output that is optimally efficient because it exploits all economies of scale but does not yet encounter diseconomies of scale.