The remap effects the engine in two ways:
1: The base map (the one you use when at steady speed) has it's fueling reduced which actually give's more power because there is more available oxygen for it to react with therfore burning more efficiently. The reasons manafactures don't run this way is that excess fuel can help with long term reliability when services are far apart by lubricating the cylinder walls. However if you service more often this shouldn't be a problem. This is where your fuel saving comes from, at any given revs less fuel is put in and more torque comes out.
2: The transient map (the one that steps in when you floor it) has it's fueling greatly increased this is to give the best aceleration when the throttle is suddenly opened and the base map cannot react quick enough to the incoming air. This means that if you drive agressively your fuel ecomomy will be worse than before but you will go quicker.
So to conclude with a remapped car if you drive slowly in a high gear at a constant speed your economy will improve usally about 10%. If you use lots of revs and accelerate constanly your economy will reduce exponentially. Power increases can be up to 40% on some turbo diesles!
Hope this helps.
