A Use Tax is a tax levied by states on items bought out-of-state which are brought into the state to be used, consumed, or otherwise utilized.
It is a way for states to collect the equivalent of sales tax for items bought out-of-state.
Note that if you paid your state's sales tax on the item, you don't report this purchase for the use tax. Also note that if the state where the item was purchased collected sales tax, then you usually don't have to report this purchase for the use tax.
If you made Internet purchases, be sure to check the receipts/invoice, because more and more Internet vendors are collecting sales tax (for example, Amazon does now in all states).