OK. First Federal (US) income taxes are one type of taxes you must file. Second, most states have state income taxes that you must also file. Depending on how much income you had, how much deductions were taken from your paychecks for each, you could possibly get a refund from one and could possibly have to pay more taxes to another. Example:
Federal tax refund: $200 (this is money taken from your paychecks that was more than your final taxes due - you would get this back from the Feds).
State taxes owed: $100 ( this means not enough money was taken from your paychecks to cover your final state taxes due - this is money you owe the state).
The two are actually filed with two different governments. Turbo tax just allows you to file both using the same program.