The Austrian School was founded in 1871 by Carl Menger, whose book Grundsätze (translated as Principles of Economics) was part of the so-called Marginal Revolution in economic thought. This marked the transition from the classical labor theory of value into the modern, subjective value theory of market prices.
The classical economists (including such thinkers as Adam Smith and David Ricardo) had a cost- or a labor-theory of value. This meant that they would explain the market prices of retail goods by reference to how much it cost to make them, and ultimately by how much labor power was “congealed” in the goods.
For example, if a bottle of wine has a market price of $100, the classical approach might explain this result by pointing out that producing the bottle used up 7 hours of manpower (at $10 per hour), $20 worth of grapes, and $10 worth of glass and other materials. This approach seemed to (generally) explain the pattern that in markets, over the long run the retail prices of goods tended to equal the cost of producing them. Furthermore, when we asked why the grapes had a price of $20, the classical economists could again list out the inputs—including labor—and their respective prices. Ultimately, retail prices would then seem to be the result of adding up all of the labor power that went into the production of a particular good, if we went back far enough in time.
However, during the Marginal Revolution of the 1870s, this approach was flipped upside down. The pioneers in this new approach said that a bottle of wine fetched $100 in the market because consumers liked to drink wine. It was the subjective evaluation by consumers of the wine’s utility that explained the price of a bottle of wine. Even if the wine producers suddenly were struck with amnesia, and couldn’t remember how much it cost to produce the hundreds of bottles in their inventories, they would still be able to go to market where prices would be determined through haggling with consumers.
To sum up: The classical economists would explain the price of wine by looking at the price of grapes. But the pioneers (who included Menger) of modern, subjective value theory would go the other way, and explain the price of grapes by looking at the price of wine. (Note that the reason farmers could charge $20 for a certain amount of grapes, is that the wine producers would be willing to pay that, knowing how useful the grapes would be in making more bottles of wine that could fetch $100 from consumers.)
The term “marginal” refers to the fact that the new approach didn’t consider entire classes of goods, but instead looked at individual units “on the margin.” (Consider that the margin on a piece of paper is at the edge.) If economists were going to explain the market price of goods by reference to their usefulness (their utility) to consumers, then marginal analysis was necessary in order to make the new approach work.
For example, water is essential to life, whereas diamonds are a luxury item. Yes typically the market price of water is very low, while diamonds are quite expensive. This initially seems at odds with a theory of prices that relies on a good’s utility to humans; if water is so important to humans, why doesn’t water have a high market value? However, we can solve the so-called “water-diamond paradox” by considering marginal utility. That is to say, one unit of water is not very important, because we (typically) have enough water to satisfy all of our uses for it. On the other hand, one unit of diamonds is very important, and that’s why diamonds are so expensive.
To sum up: In everyday market transactions, people aren’t choosing between “all the water” and “all the diamonds.” Rather, they are choosing to spend their limited dollars on particular units of water or diamonds. Thus the modern approach of subjective marginal utility can explain market prices better than the old classical approach, which relied on the flawed cost- or labor-theory of value.