Minimum efficient scale and the long-run average cost curve
To really understand the minimum efficient scale, you have to understand the long-run average cost curve since the minimum efficient scale is part of this larger curve. The long-run average cost curve shows the cost of producing a product over time, starting from when the product was produced minimally to a point where it has a high level of production.
At the beginning of the long-run average cost curve, the cost per unit is very high, and as the product is able to scale up, it eventually starts to drop. When it hits the bottom of the cost curve, or the point at which it can't be produced more efficiently or for less money, it's reached the minimum efficient scale. Unfortunately, due to things like added layers of bureaucracy, more labor, and other expansion costs, continuing to produce the product beyond this point tends to turn the curve upward again.