The AB System of Magnitudes (or AB Magnitude) sets the zero point for monochromatic magnitudes, specifically setting it so that zero represents 3631 Janskys. It can be applied to Bands through a type of averaging over the Frequency range. The monochromatic magnitude is defined as:
mAB = - 5/2 log10( fν/3631 )
A consequence of magnitudes being logarithmic is no magnitude cannot represent "zero flux" since zero has no logarithm (or it might be referred to as "minus infinity"). A brightness must be chosen to be represented by zero magnitude, which defines the magnitude's scale.
AB stands for "absolute". Other systems include the Vega System, which defines magnitudes for passbands. Exact conversion between the AB system and systems like the Vega system depend upon the Sensitivity Function associated with the passband.