My advice would to be to keep clearly separate the very specific concept of "Pareto efficiency" (which is presented in @BB King's answer and which is implied by the passage the OP quoted), with the more general term "economic efficiency", or just "efficiency".
"Pareto efficiency" is a tricky concept and criterion. The concept essentially formalizes the "limits of Economics": once an economic system reaches a point where "one man's gain" can only be "another man's loss", then any further action will have to be based either on value judgements or on the balance of socieconomic power. Economics may analyze these phenomena, but it cannot prescribe further actions under a universally acceptable criterion.
The general term "efficiency" on the other hand is used in various places in the Economics literature to essentially refer to "not wasting resources", to "using resources as efficiently as possible", i.e. in a more narrow sense, usually focused on production. This is a less ambitious, pragmatic route for economics: leave distributional matters aside, focus on maximizing production and then, it is society's burden to allocate this maximized production between its members (when Economics analyzes "inequality and growth", it examines whether inequality hurts growth and production, and not whether it is "good/bad" from an ethical or philosophical point of view).
There is a whole related subfield in Economics, with an applied focus but based on rigorous theoretical and mathematical analysis, which deals exclusively with the matter, Efficiency Analysis, which has two main branches, Stochastic Frontier Analysis (SFA), and Data Envelopment Analysis (DEA). Here, we care about whether the productive mechanisms of society "use the resources efficiently", where we look at the matter from different complementary aspects: for example,
Given the available technology, do firms produce the maximum possible output? ("Technical" efficiency)
Given technology and factor prices, do firms employ the optimal resource mix? ("Allocative" efficiency)
etc, see for example
Fried, H. O., Lovell, C. K., & Schmidt, S. S. (Eds.). (2008). The measurement of productive efficiency and productivity growth. Oxford University Press.