Giffen goods are those products whose demand, contrary to normal goods, increases with price - an upward sloping demand curve. Steve Levitt has an excellent post clarifying the recent claims that rice in rural China (peasants buy more of rice as its price rises) and prostitutes (types of customers preferring more expensive prostitutes) are examples of Giffen goods, may be off the mark.
Levitt writes, "When we talk about the demand curve for a good, what we mean is how the quantity consumed for that exact same good changes with the price of that good while holding everything else constant (such as the consumer’s income, the price of other goods, etc) and vice-versa."
In case of prostitutes, cheaper and more expensive prostitutes are two types of "goods", serving two different categories of consumers. Therefore the customer who purchases the high-price prostitute would demand just as much or more of her services if she were willing to do all the same things but at half the price.
Rice is the staple diet in rural China, whereas meat is a luxury diet, and people prefer to substitute rice with more meat (substitution effect) as they become richer. However, as the prices of commodities rice (or inflation takes hold), peasants face reduced real incomes (income effect of a price change) which turns them away from consuming luxury food items like meat and towards consuming basic staple like rice. For staples like rice, the substitution effect and the income effect push in opposite directions, and when the income effect is bigger than the substitution effect (the relative rise in price of rice is smaller than that of meat or the difference between the prices of the two products are too high), higher rice prices lead the peasants to feel so poor that they end up consuming more rice.