The study of how humans/societies allocate scarce resources.But I'm not sure what they really means, it raises more questions than it answers. Such a definition gives no real insight into what economists study and what they do. But to be fair no short definition can convey the scope and flavour of the whole subject as it has it has evolved.
The most famous definition was given by Lionel C. Robbins
Economics is the science which studies human behaviour as a relationship between scarce means which have alternative uses.The great Cambridge economist Alfred Marshall said that
... Economics is a study of mankind in the ordinary business of life; ...while Ronald Coase said
My view of economics is that it is the study of the economic system, that it studies how people earn their incomes and how they spend them, and that it studies the institutions of the economic system, that is to say, banks, markets, and firms, all influenced ... by the legal system.Ludwig von Mises said
It is true that economics is a theoretical science and as such abstains from any judgment of value. It is not its task to tell people what ends they should aim at. It is a science of the means to be applied for the attainment of ends chosen, not, to be sure, a science of the choosing of ends. Ultimate decisions, the valuations and the choosing of ends, are beyond the scope of any science. Science never tells a man how he should act; it merely shows how a man must act if he wants to attain definite ends.and
Economics is, of course, not a branch of history or of any other historical science. It is the theory of all human action, the general science of the immutable categories of action and of their operation under all thinkable special conditions under which man acts.But for me I think Steven E. Landsburg was heading in the direction when he wrote
Most of economics can be summarized in four words: People respond to incentives. The rest is commentary.However, perhaps Jacob Viner got it most right when he said
Economics is what economists do.