Curve K is designed for motor and transformer branch circuits where inrush currents are higher than resistive loads but lower than Curve D applications. The magnetic trip threshold sits between 8 and 12 times rated current, so it holds through motor starting without nuisance tripping.
This breaker carries a 15 kA interrupting rating at 230 VAC and 10 kA on DC circuits. For a panel builder coordinating downstream feeders, that 15 kA at 230 VAC gives headroom for most industrial distribution boards fed from a 100 kVA transformer — you can achieve selectivity with upstream devices rated higher without cascading the fault.