I live in Ohio, work in Kentucky. Filling out Ohio tax form, it has a thing about if another state took taxes out other than Ohio and about double taxed. What's it mean?

You should not be in that section of the Ohio program.  It does not apply to you. You are not eligible for a credit for any KY tax withheld.

Ohio has a reciprocal agreement, on wages,  with all neighboring states. No state taxes are withheld or due and you do not normally need to file a return for the other state KY. But OH will tax you on your KY..

If other state taxes are mistakenly withheld, you then have to file a return, for the other state, to get a refund. OH will not give you a credit. You should ask your employer to stop withholding so you don't have to file a , KY return every year.

Look at your W-2. If KY is not in box 15 or KY is in box 15, but box 17 is 0 or blank. You do not need to  file a KY return. In that case, in the personal info section, when it asks if you made money in another state, answer NO, per the reciprocal state instructions, on that page. This will prevent TurboTax from thinking you need to file an KY return.

If you do need to file for a KY refund, 

KY has a specific form (740 NP-R ) for a reciprocal state refund. Rather than paying TurboTax for KY software, you should try filing that form by hand. It looks pretty  simple.

https://revenue.ky.gov/Forms/740-NP-R.020521.pdf

However the reciprocity agreement does not apply to local city/county taxes. You are not required to file a local city return, but you are also not entitled to a refund of the city withholding (box19 on your W-2), unless there was an error in the amount. If you are subject to an OH  city tax, you should check to see if  your city will give you a credit for the KY city tax withheld. You cannot get a credit on the state return, only (maybe) on your OH city return.  You cannot get credit for KY city/county tax on a School District return, only on a city return.