Vehicle Tuning is achieved by taking the original parameters and changing them to something more suited to the enthusiast. Within the vehicle's ECU, is a memory section, usually a separate memory chip which stores both the program code on how to interpret and control the engine systems and also a data section, where the individual values are collected into "look up" tables. It is this reference section of tables, or "Maps", where the tuning takes place.
These are the Maps where the term Remapping comes from. The Maps are analysed, identified and modified to change the settings on your vehicle. After they are modified, the internal data self-verification function, known as a Checksum is corrected. The Checksum is a calculation taken over the contents of the file, so any alterations of the data will be recognised, and the ECU will either record a fault code, or in most cases now, refuse to operate the engine. As a Tuner makes these changes, the Checksum needs to be re-calculated so the changes are not assumed to be data corruption.

Remaps or Chips?

There is a lot of confusion as to the differences between Remaps and Chips. Both carry out the same function, and one is not inherently better than the other. Both methods extract the original Software from you vehicle, modify it, and replace it, but in slightly different ways.
The term Remap is generally used to describe accessing the data via the OBD diagnostic port, saving this to a separate computer and modifying it. The Tuned file is then reloaded onto the ECU, and the changes are made. This is also sometimes called Flashing, in reference to the Flash memory chips.
Chips have to be used when the original memory chip is not able to be reprogrammed. In these cases, the original memory chip needs to be removed and one reprogrammed with modified software is fitted. Both methods carry out the same function but use different methods of getting the new data into the ECU.
Remapping is often the "tidier" method, and in most cases can be done from the passenger seat of the vehicle, whilst remapping requires removal of the ECU, disassembly, and the physical change of the chip, either via a push fit socket or surface mount soldering.
Two further modes of Programming exist, Bench Flashing, where the ECU is removed from the vehicle, and connected to a special adaptor loom to program it outside of the vehicle environment, and BDM programming, where a special interface is used directly onto the circuit board of the ECU, which can access a larger section of the stored data. The extra data is not always needed to adequately retune a vehicle, but it can be used to clone replacement ECUs in the event of damage.
In general, vehicles before 1996 will have a Chip replacement, and vehicles after this date will be Remapped through the ODB port. There are always exceptions to this rule, so feel free to contact me if you are unsure.