A marginal tax is a tax applied only to the amount that goes over a certain limit. It is defined by both a rate and the lower limit of the amount to which that rate is applied (though the lower limit often goes unmentioned in discussions of "top marginal tax rate").
If we have a marginal tax rate of, say, 50% on income over $10,000, and no tax below that, then, for example --
- income $10,000 - tax is $0
- income $10,001 - tax is $0.50
- income $10,100 - tax is $50.00
- income $20,000 - tax is $5,000
...and so on.
Note that there seems to be much confusion about how this works; even many adult people who have been paying income tax for many years seem to be under the misapprehension that if their income goes over a certain amount, a higher overall rate kicks in and they will suddenly be paying a larger percentage of their overall income as tax -- thus resulting in losing money as a result of a rise in pre-tax income.
This misconception may be in part because the IRS generally doesn't publish the formulae by which it calculates tax rates, but only the tables by which to convert tax liability into tax amount -- making it more difficult to perceive what's going on.