What is meant by "enter amount you paid in 2016 on your 2015 state estimated taxes"

They're asking about any 4th quarter estimated payment you made to the state after the end of 2015, since that quarterly payment's deadline is in January of 2016.

Generally, folks who make quarterly estimates tend to make them at or around the quarterly deadlines.  Since that 4th quarter payment is often made in January (after the end of the year) it doesn't count toward the federal deduction for state taxes paid until the next year (a 2015 payment made in 2016 counts for the federal deduction in 2016, since that's when it was paid).

The 4th quarter state payment will still be added to the 2015 state return -- you'll get full credit for it as an amount paid in -- but for federal deduction purposes it will count in 2016.