A "local" refund would be a refund of tax you paid to your town, city, county, school district, etc. A state refund would be a refund from the state you live in.
It asks you if you received a state or local tax refund on a 1099G because if you itemized deductions on your 2022 return, that state or local refund is taxable income for 2023. If you just used your standard deduction on your 2022 return last year, you do not even have to enter a state or local refund.