Fail safe is a pre-programmed condition that your model's receiver will adopt when it loses radio signal. When the receiver is powered up but there's no radio signal, it will send pre-programmed channel positions to its connected devices.
So for instance, if you fly your plane out of range, your fail-safe kicks in - and if you've set it up right, your motor can be switched off, your ailerons/rudder will kick the plane into a wide circle, your flaps will go down, and your plane will gently descend to a hopefully relatively gentle crash landing. Or if you're lucky, you can regain control while it's circling. People also commonly use failsafe to trigger their Return to Launch function on their flight controller, for more complex FPV aircraft.
How to set it up will depend on the make and model of your radio system.