An indirect tax is one which is not collected directly form the individual or entity that is being taxed. For example, an indirect tax would include sales taxes which are collected from the retailer and paid to the government through the retailer. However, the retailer was not the originator of the tax payments. Whereas a direct tax is one which is paid directly to the government, such as income tax.
Both indirect taxes and direct taxes are eventually paid to the jurisdiction to which the taxes are due. However, indirect taxes must go through a third party before reaching the taxing jurisdiction. Indirect taxes are the responsibility of the individual or entity being taxed, but the responsibility to distribute those taxes to the appropriate tax jurisdiction, is the duty of the individual or entity that collected those taxes.
Direct taxes are paid directly from the individual or entity responsible, to the tax jurisdiction collecting those taxes. For example, income taxes are paid directly to the taxing jurisdiction. Individuals file income tax returns for both the federal and state government, when applicable. The individual then pays taxes to each individual tax jurisdiction, based on those income tax filings.
There are a variety of direct taxes and indirect taxes imposed on United States citizens. Regardless of the type of tax, the taxes eventually reach the tax jurisdiction which imposes them.