Rechipping is the replacement or reprogramming of a chip on the controller board.
The difference can be dramatic if the car has a turbo, otherwise it is minor, for Audis anyway.
Most turbos can handle some added boost but in some cases the turbo is replaced as well as some other parts.
Usually it involves removing the box containing the board and shipping it to a company to have the chip either reprogrammed or replaced.
Some manufacturers will install a small circuit board with a bit of anti-piracy circuitry.
The cost starts at around $500 US.
I have an Audi A4 1.8t which I chipped.
The difference is not noticeable when driving moderately but when you open it up in any gear, the boost is dramatically greater, like night and day.
There are several companies who offer products for Audis because many Audis have turbos.
The chips offered for non-turbo Audis are apparently not worthwhile, if they are even available anymore.
This is the website for the company whose chip I used.
http://www.hoppenmotorsport.com/
I have no idea if there are companies who modify Hondas.
