What does Economic Efficiency mean?

Answer: Economic efficiency is a term typically used in microeconomics when discussing product. Production of a unit of good is considered to be economically efficient when that unit of good is produced at the lowest possible cost. Economics by Parkin and Bade give a useful introduction to the difference between economic efficiency and technological efficiency:

There are two concepts of efficiency: Technological efficiency occurs when it is not possible to increase output without increasing inputs. Economic efficiency occurs when the cost of producing a given output is as low as possible.

Technological efficiency is an engineering matter. Given what is technologically feasible, something can or cannot be done. Economic efficiency depends on the prices of the factors of production. Something that is technologically efficient may not be economically efficient. But something that is economically efficient is always technologically efficient.

A key point to understand is the idea that economic efficiency occurs "when the cost of producing a given output is as low as possible". There's a hidden assumption here, and that is the assumption that all else being equal. A change that lowers the quality of the good while at the same time lowers the cost of production does not increase economic efficiency. The concept of economic efficiency is only relevant when the quality of goods being produced is unchanged.