The marriage penalty in the United States refers to the higher taxes required from some married couples, where spouses are making approximately the same taxable income, filing one tax return ("married filing jointly") than for the same two people filing two separate tax returns (as single, not "married filing separately"). The percentage of couples affected has varied over the years, depending on shifts in tax rates.
The source of this increase in taxes has its roots in the progressive tax-rate structure in income-tax laws, that is, a higher income pays a higher rate of tax. In such a context income averaging is advantageous to the taxpayer. E.g. two persons, one making $80,000 and the other making $20,000 in a particular year, will pay a larger combined tax than they would if both had an income of $50,000 in the same year.
Married couples normally combine their income which, when the spouses' monetary incomes are disparate, affords them the advantage of this income averaging. To compensate for this somewhat, the U.S. income tax law provides for somewhat higher tax rates on that averaged income (married couples pay more than twice the tax of a single person making half of the income) for the "married filing jointly" taxpayer class. So although couples with disparate incomes (which is the case for a stay-at-home spouse married to a "breadwinner") will gain a tax advantage from the income averaging, married couples having roughly equal personal incomes gain nothing from such income averaging yet remain subject to the higher tax bracket (for "married filing jointly") and thus pay more total tax than they would as two single persons.
Occasionally, this "marriage penalty" has become a campaign issue for various candidates and there have been piecemeal laws enacted to reduce it, none completely successfully.

This so-called marriage penalty showed up in 1969, when Congress tried to equalize what was then an unfair advantage couples held over single taxpayers. [1]
Several years ago, forty-two percent of married taxpayers paid more because they were filing jointly than they would have if they remained single, according to a 1996 Congressional Budget Office analysis. The average penalty was a significant $1,380. [2] Several pieces of legislation have been passed since the late nineties to do away with these penalties. However, through passing those pieces of legislation, the tax system is now such that many couples will experience a marriage benefit.