The demand for any good is derived from the optimal quantity of that good which would be chosen by consumers at every given price. The resulting relationship gives quantity demanded as a function of price. For most goods (but not a Giffen good), the demand curve is downward-sloping, with decreasing quantities demanded as the price increases. Aside from slope, the chief properties of a demand curve are its elasticity and curvature. Both address the rate at which quantity demanded varies with price, and how this rate might change.
The demand curve represents a simple relationship. It tries to demonstrate how many items of a product or service a consumer would like to purchase at different prices. 
Demand Shift - The demand curve introduces price for the first time as the common denominator. The law of demand yields an inverse relationship. We distinguish between changes in quantity demanded, movements along a single demand curve caused by price changes, and shifts in the entire curve caused by a change in a factor other than price. The demand curve represents marginal benefit but average revenue. 
As a non-economic verb, demand can also mean to refuse or strongly imply or pressure or persistent begging. Example, the robber demands the money in the vault.