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.