In an economic sense, the ratio or proportionality between the value of the human end achieved ("benefits" or "satisfactions") and the value of the scarce resources expended to achieve it (opportunity costs). When an economist calls a situation or a practice "inefficient," he is claiming that we could achieve exactly the same desired goals with the expenditure of fewer scarce resources, or, put another way, that the amount of resources being employed could potentially produce even more of the beneficial results intended than they do. Efficiency simply means making the most we can of the limited resources we have.
Notice that "efficiency" in the economist's sense is an inherently evaluative term, not a matter of mere technical or scientific measurement of objective physical quantities, as the term might be used in an engineering context (as for example, the "efficiency" of various kinds of steam engine in transforming heat energy to useful kinetic energy). "Value of" always requires some sort of answer to the question "value to whom." When we assess the efficiency of any process or social institution or practice, just whose evaluations of the means and the ends are we using? In a well-developed market economy, assessment of economic efficiency makes heavy use of the monetary values placed on the various inputs and the resulting outputs in the open marketplace. The valuations that count are thus the valuations of those who are willing and able to support their preferences by spending their money in the ways that seem to them most likely to maximize their own satisfactions or "utility" based on their own individual tastes and preferences. The evidence that any particular economic resource is being used efficiently is, in the end, the fact that no one finds it "worth his while" to bid up the price and pay more in order to divert it to some other use.
The logical and philosophical elaboration of the idea that competitive market systems are highly efficient in a much broader sense even than this is the primary content of Adam Smith's classic work The Wealth of Nations (1776). Indeed the entire subdivision of today's economic science known as "welfare economics" specializes primarily in identifying and analyzing the necessary preconditions for voluntary market interactions to generate socially efficient outcomes (and in examining the possibilities for remedies by deliberate state economic policies where those necessary preconditions may not be fully met).