I think I'm being a bit thick here, but are adaptations the personal settings you do though the BCU?
they are controlled through the ecu
the adaptions are for the fuelling , as I understand it you have short term and long term trims .
while you are driving the fueling is controlled using all of the info from the various sensors , speed , gear , throttle position , engine temp, lambda etc
while driving normally the engine is in a 'closed loop' state , it monitors the sensors , squirts in the fuel , then measures the gasses in the exhaust (lambda) , if they are too rich (unburnt fuel ) it adjusts the short term trims to make the fuelling leaner.
If they are too lean then it adds more fuel by adjusting the trims.
it does this several times a second.
if the short term trims cant adjust quickly enough then it adjusts the long term trims so the base setting is closer to where it needs to be and the short term trims aren't working so hard. the general name for this is the adaptions
problems occur when a sensor fails , if it gives the wrong reading then the ecu will try to fuel according to the wrong reading and over time the fuelling will be way out which will lead to poor economy and loss of power.
resetting the adaption puts it back to factory settings .
If you run an lpg system which uses the ecu settings then the adaptions will need resetting periodically as lpg burns differently to petrol and puts the trims out.
sorry if thats a long winded explanation , someone may be able to explain it a bit better
Andy