I believe the ECB's interest rate is currently 0 or 0.5%, and thus the Danish National Bank's interest rate is negative to maintain the DKK loosely pegged to the EUR. This means, it costs money for regular banks to have their customers' money at the National Bank, and therefore offsetting the cost to their own costumers.
Initially, the limited was 750'000 DKK before the negative rates would kick in, then 250'000 and now 100'000. Danske Bank is hardly alone in this, a lot of other Danish banks have already done the same. The slow lowering of the limits is indicator that the banks more and more believe that the negative rates at the National Bank will remain with no end in sight.
Disclaimer: I am not an economist.