A tax that is not paid directly to the government, like income tax, but through another medium involving choice, such as buying goods which have VAT charged on them. See Direct Tax.
You might not think you're paying this tax, but you probably are. It's the type of tax that can be shifted to others: hence the name. For example: A company might have to pay a specific tax to the government, let's say a fuel tax. The company pays the tax but can increase the cost of their products so consumers are actually paying the tax indirectly by paying more for the company's products.
A tax for which you are not directly responsible and can be passed on to others. Example, business property taxes.