The MAF is generally implyed to mean the Mass Air Meter as a whole though it literally stands for Mass Air Flow. In the theory that the engine is nothing more than a big air pump, the most air you can get through the engine at any given time is determined by the most restrictive passage during its travel. Sometimes this point is the MAF. You would get a larger MAF (meter assembly) when you have sufficiently enlarged other portions of the engine to determine this as a choke point in need of enlargement.
How the MAF is "recalibrated" it is determined by the manufacturer. Pro-M requires you so replace the entire black sensor plate while others simply require a different sampling tube. The MAF is calibrated to your injectors so if you change injector size you need to "recalibrate" your MAF.
The MAF is simply there to determine air volume and temperature as it enters the engine. There is a small coil that is heated by passing electricity through it until it reaches a certain resistance. The amount of electricity required varies due to the cooling effects of the air passing over this coil as it enters the engine. The more air, the faster it cools thus requiring more electricity. Some smart guy figured out a whole range of resistance that cooresponds to air volumes and temps. The value determined at the MAF is sent to the computer which then puts it through another formula to determine the pulse width the fuel injectors need to dish out in order to satisfy that amount of air. Put a larger fuel injector in there without recalibrating your MAF and you're dumping too much fuel in.
So... you recalibrate your meter so it throws out a different value that now cooresponds to your new injector size.