A cabinet of 4/8/16 etc impedance ( in ohms ), refers to the net/resultant voice coil impedance of the cabinet. If a 2x12 cabinet is connected as follows 2 8ohm ( voice coil impedance) speakers in series then your cabinet impedance is 16 ohms. if they are arranged in parallel it would be 4 ohms.
Cabinet impedance should match with that of the head. some Amps are capable of delivering different output powers based on the output impedance to which it is connected. For eg an amp can deliver 40Watts RMS @ 8 ohms load and 60watts RMS @ 4ohms ( provided your transistors/tubes/FETS can handle this increased current and your power supply can source the additional current ) .
Amplifier specs will mention this.