The foreign tax credit’s purpose is to reduce the double tax burden that would otherwise arise when foreign source income is taxed by both the U.S. and a foreign country from which the income is derived. Typically, the foreign tax credit is a dollar-for-dollar reduction for all foreign income taxes paid. However, it only reduces U.S. federal income taxes (as opposed to, e.g., employment taxes or federal excise taxes). Note also that the alternative minimum tax (AMT) has its own special FTC.
If the foreign country taxes at a lower rate than the U.S. rate, then the taxpayer receives a full tax credit on the foreign tax. However, the taxpayer must pay the difference to the U.S. government. However, if the foreign country taxes at a higher rate than the U.S. rate, the taxpayer will not be required to pay any U.S. tax; the taxpayer will simply pay the foreign country’s tax rate.