FEC
Flash Exposure Compensation (FEC) is very similar to exposure compensation that you may know already from shooting with ambient light.
When you use a flash, the flash is typically the dominating light source and if you find that the flash light is either too strong or too weak, the remedy is to adjust the light via flash exposure compensation.
Why not set the flash power manually? Indeed, that is an option, but if the lighting conditions change, then the manual settings need to be adjusted accordingly, and that requires a bit of adjustment. If you have the flash exposure compensation engaged and the light conditions change, the automated reading of the light will factor in the change. Just like exposure compensation, FEC pushes the automated reading of the light either above or below the automated reading.
You set the flash exposure compensation in stops of light. My Godox V860iii allow that up to 3.0 stops of light are added or subtracted.
You will typically use FEC when you are not happy with the automated exposure, but don’t want to switch to manual flash power. It can also be that you are happy with the exposure or find that it is just right, but want to make say a high key image where the exposure is deliberately adjusted.
Related reading
What is a camera’s max flash sync speed?
Can a flash zoom? And what is the point?
Review: Godox V860 III Speedlite flash