when you enter a higher cruise C of G value (up to a point), it effectively shifts the lift vector closer to the weight vector. This in turn requires less downward force on the rudder and hence reduces the effective 'weight' of the aircraft
The CofG value in the FMC is in %MAC. Higher values indicate a rearward CofG, lower values a forward CofG. The weight vector moves with the load, not the lift vector. Entering a higher CofG value into the FMC tells the FMC that the load is distributed rearward.
The horizontal stabiliser and elevator normally produce a balancing "down" force in the cruise. A rear CofG requires less force (the weight being closer to the tail) and a forward CofG requires a higher force (weight away from the tail.) If the CofG is forward, the higher down force being produced by the tail must be countered by a higher angle of attack (and consequent induced drag) from the wing - so the performance is better with a rear CofG and worse with a forward one. Some airlines have load policies to take advantage of this and load the aircraft holds from back to front to move the CofG as far back (within the limits) as possible.
The default value on the FMC is simply the most limiting (forward) CofG case. While the methods above are accurate, the differences are so small that (on the 737) I usually enter a figure half-way between the take-off CofG and landing CofG shown on the load sheet.