It's all in the AFM supplement for the particular box installed on the type. A typical FMC/FMS manufactured after the mid nineties is going to use totalizer quantity, current fuel flow and ground speed to predict fuel remaining for a given distance down route, then "ramp" or "blend" the expected fuel flow according to a performance model programmed in the box thereafter.
The predictive performance models in the box will consider the forecast winds & temps entered in the FPLN for each fix to calculate the fuel remaining at each fix all the way to destination. The altitude and airspeed/mach number applicable between each fix will be a default value unless a manual entry is made. This is of course most accurate when all fixes have forecast values and the forecast itself is reasonably accurate.
An older Honeywell box (FMZ-2000) on a Hawker I used fly ramped/blended the current fuel flow and speed to the values 700 NM down route. So the predicted fuel remaining at each fix on the FPLN route was a blended value between present position and 700 NM ahead, and purely according to the calculated predictive values thereafter.
It works a charm too. It was typical in the Hawker to see less than 2% difference between FMS predicted and actual fuel burn on a 6 hour flight. The greatest part of any error is generally attributable to wind/temp aloft forecast accuracy and whether the climb and descent profiles were flown as programmed in the box. ATC can't always allow that given the vagaries of traffic and weather.
In addition to supporting gross error detection, constantly comparing the box predictions with mental math derived calculations has the benefit of giving one something to do on longer sectors, thus maintaining a somewhat higher level of consciousness, especially in the wee hours.
I hope the above encourages anyone curious about the FMC they operate to crack open the supplement if available.