This one is right up my alley.
First, inverse time is another name for thermal magnetic. It means that if there is a lot of current, such as a short circuit, the magnetic or instantaneous portion of the characteristic will open the breaker fast. An overload would activate the thermal portion and will take a bit more time to trip the breaker open. So the amount of current is inversely proportional to the time it takes to trip.
There are many different adjustments available from different model/style breakers. Instantaneous adjustments are very helpful in reducing arc flash incident energy and protection of a motor during startup (allowing the protection characteristic to more closely follow the starting current without tripping). The long or short time is adjusted, along with instantaneous, to assist in the OCPD closest to the fault/overload to trip first (selectivity).
