In the context of the oil industry, "demand" generally refers to the quantity consumed (see for example the output of any major industry organization such as the International Energy Agency), rather than any measure of a demand curve as used in mainstream economics.
The term has come to some prominence lately as a result of the growing interest in the peak oil theory, where demand destruction is the reduction of demand for oil and oil-derived products. The term is used by Matthew Simmons, Mike Ruppert and other prominent proponents of the theory. It is also used in other resource industries such as mining.
A familiar illustration of demand destruction is the effect of high gasoline prices on automobile sales. It has been widely observed that when gasoline prices are high enough, consumers tend to begin buying smaller and more efficient cars, gradually reducing per-capita demand for gasoline. If the price rise were caused by a temporary lack of supply, and the price then subsequently goes back down as supply returns to normal, the quantity consumed in this case does not immediately go back to its previous level, since the smaller cars that had been sold remain in the fleet for some time. Demand thereby has been "destroyed"; the demand curve has shifted.
The expectation of future prices and their long-term maintenance at non-economic levels for a certain quantity of consumption also affects vehicle decisions. If the price of fuel is so high that marginal consumers cannot afford to do the same mileage without switching to a more efficient car, then they are forced to sell the less efficient one. A glut of such vehicles causes the used market value to fall, which then increases the depreciation expected of a new vehicle, which increases the total cost of ownership of such vehicles, making them less popular.