Changing interest rates affect consumers most directly by changing the price that consumers must pay when they borrow money. Consumers in countries like the United States typically take out loans in order to buy very big items (like houses, cars, or boats). Changing interest rates affect the true price of these items. If interest rates go up, for example, consumers effectively pay more for a car because they are likely to have to pay a higher interest rate on their loan.
Consumers who do not buy such "big ticket" items, or those who do not need loans to buy them, are much less affected by changing interest rates.