Individual demand curves can be thought of as a set of price-quantity combinations that each represent a separate consumer optimum for different market prices. This can be seen in the diagrams below:
Point 'a' in the left diagram represents a bundle of goods (x and y) that will maximize the consumer's level of satisfaction for a given set of market prices (P0x,P0y) and income (I0). This same point in the right diagram represents an identical quantity of good-x demanded at a current price P0x. As the price of good-x declines [click on the next button] the consumer is willing (via the substitution effect) and able (via the income effect) to purchase more of good-x. The inverse relationship between prices and quantity trace out the individual's demand for this commodity. The slope of this individual demand relationship depends on the magnitude of the total effect of the price change and specifically the strength of the income effect. Stronger income effects (assuming normal goods) lead to flatter demand curves.
Additionally, this reduction in prices makes the consumer better off as shown in the tangencies to higher indifference curves in the left diagram. This increase in consumer welfare can be measured by the corresponding change in consumer surplus as shown in the below right diagram.
We can conclude our discussion by deriving a market demand curve. This market demand represents a (horizontal) summation of individual demand curves. Specifically, for each market price, individual consumers each have their own consumer optimums and corresponding demand for the good in question. We add up these demand for each possible market price to calculate the total quantity demanded in the market. It is the sum of these individual demand curves -- the Market Demand curve that we use in our analysis of market behavior. For example:
Thus, we find that in the market, every time the price is reduced by $0.50, the total quantity demanded (market demand) increases by 6 units.