Please correct me if I am wrong, but I feel this is what he is trying to say:
You have a poti and its rotation is 0%-100% (0-1023), BUT your only using 25% of that rotation your only getting ~255 ADC points.
What he seems to be getting at is that since you are only using 25% of the poti's rotation, to get higher "accuracy" of that 25%, to have a "little thingy" that takes that 25% of poti rotation, and scales it with finer points to the 0-1023. In essence taking the 25% rotation of the poti and making it the NEW 0-1024 ADC value.
I believe this is what he is getting at. So it's a scale-er of some sort.
So if the above is correct... and as an example, he has a poti and only 25% of that rotation is being used. Lets just take for example that his poti outputs, due to its use in his application, 2V -> 3.25V (Roughly 255ADC points, or 1.25V of change). His "little thingy" would take that 2V-3.25V of change and output 0-5V based on only 1.25V of change. In essence breaking that 1.25V of change into finer segments for the ADC of the arduino to use.