The statement that something “costs an arm and a leg” is an idiomatic expression in the English language. It is a way of implying that the desired object or situation has a very high cost — of such magnitude as to be prohibitive or absurd. The saying is one of the more common idioms used in English.
The phrase finds use in several situations. It often is used to describe the price of a needed commodity or service that may not have a prohibitively high cost but a price that seems to be consistently elevated or on the rise. Many people tend to refer to gasoline as costing an arm and a leg for this reason. In many places around the world, it is possible to purchase fuel on a typical motorist's income, but it nevertheless has the reputation of being expensive.
On other occasions, the expression “costs an arm and a leg” is used to reference items that, in fact, do have a very high cost, so much so that they cannot be acquired except only by the richest of people and perhaps not even by them. The items referenced can be luxury items such as cars or houses that could be purchased by a wealthy person. It is possible, though, that the items being referenced simply cannot be purchased.
The origins of the phrase are somewhat unclear, although it is surmised that the “arm and a leg” theory originated during times prior to photography, when paintings were a common way of portraying people. Usually, the larger the painting, the more it would cost. The least expensive portrait would be a painting from the shoulders up but, if the person’s arms were shown, it would mean a larger painting; if the legs — and, thus, the entire body — were shown, it would be bigger still. Thus, any painting that showed a person complete with arms and legs would likely be large and, as a result, quite costly.
There is some thought about the saying having originated somewhat later, particularly during World War I. The loss of an arm or leg in that conflict was not uncommon and would certainly be considered a very high cost — though not a financial one — to a war veteran. Some speculation considers the war explanation and the loss of both an arm and a leg as particularly severe, or something that is an especially high cost.