As per utility theory, consumers allocate their total available disposable income in such a way that the the utility or satisfaction derived per dollar spent on the last unit every good is same. Under this condition, the consumers are able to maximise the total utility from the total money spent by them.
When the price of any single product in the basket of goods purchased a consumer changes, the satisfaction per dollar spent on the last unit of that good purchased also changes. In case of price increase the utility per dollar will reduce, and therefore the consumer is likely to reduce the consumption. When the price decreases the reverse happens. The exact relationship of price changes and corresponding changes in demand will depend on demand elasticity.
Of course, with changes in price and demand of one product, the income available for other products will also change. With all these changes a new equilibrium points will be found.