Taxes assessed under a progressive system are based on the taxable amount of an individual's income. They follow an accelerating schedule, so high-income earners pay more than low-income earners. Tax rate, along with tax liability, increases as an individual's wealth increases. The overall outcome is that higher earners pay a higher percentage of taxes and more money in taxes than do lower-income earners.
This sort of system is meant to affect higher-income people more than low- or middle-class earners to reflect the presumption that they can afford to pay more.