The opposite of a progressive tax is a regressive tax. In this case, the amount of the tax is smaller as a percentage of income for people with larger incomes. Many taxes other than the income tax tend to be regressive in practice: e.g. most sales taxes (since lower income people spend a larger portion of their income), social security taxes (because they exclude interest, rent, and other kinds of income common for the affluent), excise taxes, and so on. (A flat tax, also called a proportional tax, is one where the tax amount is fixed as a function of income, and is a term mainly used only in the context of income taxes.)
The argument for a progressive tax system is that people with higher income tend to have a higher percentage of that in disposible income, and can thus afford a greater tax burden. A person making exactly enough money to pay for food and housing cannot afford to pay any taxes without it causing material damage, while someone making twice as much can afford to pay up to half their income to taxes. The converse argument is that too progressive a tax rate acts as a disincentive to work; in the previous (extreme) example, there would be no monetary incentive at all for the first person to try to double his or her income.
For example, in the United States there are six "tax brackets" that are used to calculate the percentage of income that must be paid as income tax to the federal government. These percentages in 2003 and 2004 are:
Tax progressivity or regressivity should not be confused with two similar concepts: tax neutrality and tax incidence. Tax neutrality refers to the effect a change in taxation policy will have on government revenues. If the change has no net impact to government income, it is said to be neutral. Tax incidence refers what group ultimately bears the burden of a tax (for example, sales taxes, which are nominally applied to businesses, are passed through to consumers as higher prices), and can measure the effective progressivity of a tax by income group as well as breaking the impact down by geographic area or other factors.