Fail secure means that if the power is interrupted or fails, the door stays locked. That's why it's called "secure"-- its default state is locked or secured. A fail-secure door locks the door when power is removed. Power is required to unlock the door. Fail-secure locks keep the doors secure even when no power is applied.
Often fail-secure locks are used for IT rooms or other sensitive areas. However because the door remains locked in emergencies, typically it will be usable with a mechanical override, such as a regular key. However, this is also a way of getting in the door without leaving any electronic traces. In situations like this, the use of mechanical override keys is often restricted to only a few people who are highly restricted in its use.
Fail secure locks are used for fire-related doors or stairwell doors. In case of fire, those doors should remain closed to seal off a portion of the space and help prevent the fire from spreading. Fire doors require fail-secure electric strikes for positive latching. Fail secure locks are the most commonly used electronic locking device for high-security situations because their default state is to remain locked.