Settling time is the time an opamp takes to settle on it's output (to a % accuracy) after a step response (usually) is input.. or
Time for your opamp to settle down within a specified output range(accuracy), usually within 0.1% error.
The accuracy to which it has to settle within the settling time depends on the application. If the opamp is used in an adc for example, you'll have one accuracy requirement if the adc is 8 bit and quite different if it was 12 bit.