Class AB is just a combination of Class A and Class B.
In pure Class A, the output device(s) conduct over the full signal cycle. The bias is set so about half the maximum current is passed when no signal is present. When a signal is applied, it modulates the current below and above the mid point up to a maximum swing of ground and supply (fully biased on and off). Arguably it gives lowest distortion but running the output stage at an average of half power all the time is very inefficient.
In pure Class B, the output devices only conduct for one half of the signal cycle and have no bias on them at all. It would be nice if transistor were completely linear devices but they aren't. This means that during the smallest part of the signal, the transistors will still be working in their 'turn on' region of between zero and 0.6V where very little conduction takes place. It causes what is called 'cross-over distortion', a region just above and below zero where nothing happens. As the signal increases above the transistor threshold, the transistors conduct and everything works fine. It is very efficient because with no signal present, the current consumption is zero.
Class AB is a mixture of the two. The transistors are biased to conduct enough to overcome the turn-on voltage so the cross-over distortion is eliminated but not much more. At low signal level it is effectively the same as Class A. When the signal increases, it becomes the dominant source of bias and the transistor start to conduct more, this is like Class B. So AB isn't quite as efficient as Class B but it doesn't suffer from distortion and it is still greatly more efficient than Class A.
Consider this example, these are made up numbers so don't judge me on math!
Class A - current consumption a steady 1 Amp
Class AB - small signal consumption 20mA, large signal 1 Amp
Class B - small signal consumption zero, large signal 1 Amp (but distorted at small signal)
Brian.