Origins
The word "demand" entered English around 1290 from Old French "demander" (to ask, to request), from Latin "dēmandāre" (to entrust fully, to give over to someone's charge), composed of "dē-" (away, completely — here serving as an intensifier) and "mandāre" (to order, to commit to one's charge), from "manus" (hand) + "dare" (to give). The etymological image is of placing something completely into someone's hand — entrusting fully, with nothing held back.
The word underwent a significant semantic shift between Latin and English. In Latin, "dēmandāre" meant to entrust or to delegate — a neutral act of placing responsibility in someone's hands. In Old French, "demander" softened to mean simply "to ask" — and in modern French, it retains this mild sense. "Je vous demande" means "I ask you," with no implication of forcefulness. But in English, "demand" hardened to mean asking with the force of authority, right, or insistence. To demand is not to ask politely but to claim — to place a requirement in someone's hand that expects compliance.
This divergence between French "demander" (to ask) and English "demand" (to insist) is a classic example of semantic drift: two words from the same source acquiring different intensities in different languages. English speakers learning French are often surprised that "demander" is the standard word for asking any question, and French speakers are equally surprised that the English "demand" sounds aggressive.
Development
In economics, "demand" took on its most influential modern meaning in the 18th century. Adam Smith, David Ricardo, and their successors developed the concept of supply and demand — the forces that determine the price and quantity of goods in a market. "Demand" in economics means the quantity of a product that consumers are willing and able to purchase at a given price. The "law of demand" states that, all else being equal, higher prices reduce demand and lower prices increase it.
The economic sense preserves the etymological force in an interesting way. Consumer demand is not a polite request — it is a forceful claim backed by purchasing power. When demand is high, consumers are effectively commanding producers: "Make more of this. We are willing to pay." The invisible hand of the market is, in a sense, the "manus" of the etymology — the hand that gives and takes in the marketplace.
In law, a "demand" is a formal claim asserting a legal right. A "demand letter" notifies someone that they owe a debt or obligation and requests payment or action. "On demand" means payable immediately when requested — a "demand deposit" (like a checking account) can be withdrawn at any time. These legal uses preserve the word's sense of authoritative insistence.