Although this is generally a true statement, it is not alway true.
In general, people do demand more of a product when it is at a low price and less of it when it is at a high price.
However, it is at least theoretically possible to have a product for which demand is perfectly inelastic. For such a product, people will buy the same amount regardless of the price. Here, the demand curve is vertical.
It is also possible for a product to have perfectly elastic demand where people will buy a given product, but only at one price. Here, the demand curve is horizontal.
Demand curve is a graph representing the quantity of a good demanded by consumers at different prices. In this graph the demand is represented on x-axis while the price is represented on y-axis. In general, people will be willing to buy more of a good when the price are high and less when the prices are high. This kind of behavior of demand results in a downward sloping demand curve.
The slope of demand curve is more steep when a small drop in prices results in substantial rise in demand. Conversely the demand curve will be less steep when even a large drop in price results in small increase in demand.
Theoretically a demand curve can be a vertical line when people are likely to buy the same quantity of the good irrespective of price. Goods like some life saving essential drugs can have nearly this kind of demand curve. The other extreme of demand curve is a horizontal line. Which means that with even the slightest increase in price the demand drops to zero. This is the kind of demand curve faced by a supplier in a perfectly competitive market.