McCulloch v. Maryland established that Congress has the power to incorporate banks. The case also established that the state of Maryland did not have the power to tax the bank.
In the period prior to the ruling, some states taxed banks that were not chartered by the state. The states opted to do this to place the blame for a failing economy on the banks and not the government.
When Maryland attempted to tax the Bank of the United States, which was not chartered within the state, the bank chose not to pay. In return, the state filed suit against the bank's cashier. The U.S. Supreme Court sided with the bank.