remap.basically all cars have a map on their ecu, all the same map, i.e, all 197 clios will leave the factory with the exact same fuelling map, these are factory set to give the best mpg, emissions without losing too much power.
now a re-map, is in my opinion, where someone who knows what they are doing, gets the best out of the fuelling map on the ecu, for the engine its running, i.e. most 197s will need a slightly different map to any other 197, due to tolerances in manufacturing the engine etc. there are the off the shelf chips, which are generic and only give limited results on limited engines.i.e not all 197s with the same off the shelf chip will give the same results..
re-map is getting the optimum out of your fuelling map for that specific engine, whilst also getting good emissions, and could also get better mpg, and more power.