Solid state devices (ie: output transistor) work by using the base current to control the collector current. Vacuum tube devices (ie: power tube) work by converting a voltage input into an output current.
With respect to SOLID STATE devices:
CLASS A bias means the device base current is set to allow collector current to flow through the device. This basically means there is current flow at all times, regardless of signal input.
CLASS B bias means the device base current is set to zero and therefore NO collector current flows through the device and the device is cut-off. When an input signal is present the base current will lift and allow collector current to flow and the device is now conducting.
With respect to VACUUM TUBE devices:
CLASS A bias means the grid voltage is set to allow anode current to flow at all times.
CLASS B bias means the the bias point has been set to a point where the tube has almost stopped conducting. This results in a larger input signal being required to drive the tube and an output current for only half of the waveform. To amplify each half of the waveform it is necessary to use 2 tube devices in a "push pull" arrangement, with one device taking care of one half of the waveform and the other device taking care of the the other half.
CLASS AB bias is somewhere in between the above 2 classes with usually a small amount of bias applied
The subject needs more than a quick simple explanation to understand. I hope the above reads OK and I have not further confused anyone..??
Regards, Richard.