I'm not sure I understand what an overpayment is as far as state taxes. Nor do I understand applying it to next year.

[AmandaR1 · Accepted solution]

An overpayment means you have a refund of state taxes (your withholdings from paychecks were more than the amount of tax calculated now on your return). The state sends you this "refund" of money. If all of your income comes from a job, you will typically say "no" to applying it to next year. 

Applying the refund to next year is for people that work for themselves or have income that taxes aren't withheld from, and so they need to pay as they earn. This allows them to easily have the refund sent to the state as an estimated tax for next year. You'll typically be aware if this applies to you.