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Territory taxes are taxes paid to US Territories. You may find a list of US territories here - http://en.wikipedia.org/wiki/Territories_of_the_United_States
You may view Territory taxes as kind-of state taxes but paid to the US Territory and not to the state. Territory taxes besides income taxes may include other types of taxes - sales tax, excise tax, etc.
If you owe taxes to any US territory - that debt would be treated the same way as you would owe taxes to any state - and the tax relief payment will be garnished to satisfy that debt.
Local taxes imposed by the local governments are not considered as territory taxes. if you owe taxes to any local government - either within any state or any US territory - your tax relief payment may not be garnished to satisfy that debt.