The relay in a protection system should be sensitive enough to operate when a fault occurs.  A sensitive relay improves the reliability of the system.

When the parameter exceeds the set value, the relay should start operating.

The sensitivity of a relay is mentioned as a ratio of the minimum value of short circuit current to the minimum value of the quantity for the operation.

The sensitivity is indicated by a sensitivity factor Ks

Sensitivity of a Relay
where

Is is the minimum short circuit current in the zone and
Io is the minimum operating current for the relay.

The sensitivity of a relay is also related to the VA of the input to the relay.  Lesser the VA of the input, greater will be the sensitivity and vice versa. For instance, a relay which has 1 VA as its measuring input will be more sensitive than a relay, which has 5 VA as its measuring input.