A progressive tax system is when the proportion of tax liability rises as an individual or entity’s income increases. Tax burdens are meant to be more of an imposition to wealthy, high-income earners than they are to low- or middle-class individuals. The current federal income tax is a progressive tax.
A flat tax is the same tax rate to taxpayers regardless of income or wealth – this is the same tax that Rand Paul and some of the other 2016 presidential candidates have proposed.
A regressive tax is generally a tax that is applied uniformly. This means that it hits lower-income individuals harder. Rather than implementing a tax liability based on the individual or entity’s ability to pay, the government assesses tax as a percentage of the asset that the taxpayer purchases or owns. Some examples include gas and cigarette tax.