If the quantity demanded of a certain good responds only slightly to a change in the price of the good, it means that

If the quantity demanded of a certain good responds only slightly to a change in the price of the good, it means that the demand is inelastic, which means that changes in prices would almost not modify quantity demanded by consumers. Consumers are little affected by changes in prices. This usually happends when there are no substitutes for the good. If the good has many substitutes, and the price goes up, consumers have the opportunity to swich their consumption to an alternative good. A common example of inelastic demand can be insuline for diabetes patients (or another needed medicine with no substitutes) : no matter what happens with the price of the product, usually consumers are willing to consume the same quantities although prices are higher because they really need the product.