CLASS 'A':
Many class A amplifiers use the same transistor(s) to reproduce both the top and bottom halves of the audio waveform. In this configuration, the output transistor(s) always has current flowing through it, even if it has no audio signal (the output transistors never 'turn off'). The current flowing through it is D.C. A pure class 'A' amplifier is very inefficient and generally runs very hot even when there is no audio output. The current flowing through the output transistor(s) (with no audio signal) may be as much as the current which will be driven through the speaker load at FULL audio output power. Many people believe class 'A' amps to sound better than other configurations (and this may have been true at some point in time) but a well designed amplifier won't have any 'sound' and even the most critical 'ear' would be hard-pressed to tell one design from another.
Note:
Some class A amplifiers use complimentary (separate transistors for positive and negative halves of the waveform) transistors for their output stage.
CLASS 'B':
A class 'B' amplifier uses two transistors (or two groups of transistors). One transistor (or group of transistors) is used to reproduce the top half of the waveform. A second transistor (or group of transistors) is used to reproduce the bottom half of the waveform. In a class 'B' amplifier, there is typically no idle/bias current flowing through the output transistors when there is no audio. In most cases, if the amplifier has no bias potentiometers and it's not a class D amplifier, it's a class 'B' amplifier.
CLASS 'AB':
Class 'AB' amplifiers use two groups of transistors like class 'B' amplifiers. In most respects, class 'AB' and class 'B' amplifiers are very similar. As we said earlier, a class 'A' amplifier is very inefficient. This is not good for a car audio amplifier. Some people believe that class 'B' amplifier can never produce clean audio because their output transistors aren't biased 'on'. A class 'AB' amplifier is generally considered to be the best compromise. A class 'AB' amplifier is a class 'B' amplifier which has a small amount of 'bias' current flowing through the output transistors at all times. This eliminates virtually all of the crossover distortion that's possible with class 'B' amplifiers. The bias current is flowing because the output transistors are always conducting current (even without an audio signal). This differs from a pure class 'A' amplifier in the amount of current flow. A pure class 'A' amplifier typically has an enormous amount of current flowing through its output transistors with NO audio signal. A pure class 'B' amplifier has NO current flowing through its outputs with no audio signal. A class 'AB' amplifier is much more efficient than the class 'A' but without the possible distortion of the class 'B'. MANY of the car audio amplifiers which claim to be a class 'A' amplifier are just a high bias class 'AB' design. These amplifiers are only class 'A' at very low power output levels. At higher power levels, one of the output transistors will switch off while the other output transistor is conducting. I don't want you to think that I am telling you that there are no class 'A' amplifiers. There are a few high quality mobile amplifiers which are a true class 'A' design.
CLASS 'D':
We said that class 'A' amplifiers were VERY inefficient. Class 'AB' amplifiers are also inefficient but are more more efficient than class 'A' amplifiers. Class 'AB' mobile amplifiers are generally 60% efficient when driving a 4 ohm load at maximum power (just before clipping). The reason that these amplifier configurations are inefficient is because there is a difference of potential (voltage) across the output transistors and current flowing through the output transistors. When you have voltage across the device and current flow through the device, there will be power dissipation in the form of heat. The Ohm's Law formula P=I*E expresses this clearly. The power needed to produce this heat is wasted power. When there is (virtually) no voltage drop across a device (whether it's a large piece of wire or a transistor), there can be a significant amount of CURRENT flow through the device with (virtually) no power dissipation. This means that there is virtually no heat given off (highly efficient). The inverse is also true. If you have a significant amount of VOLTAGE across the device (transistor, wire...) but no current flow through the device, again, there will be no wasted power. If you look at the formula P=I*E again, you can clearly see that if you reduce either I or E (I is current, E is voltage) to a value near 0, the power dissipation will be very low.
OK, now to the point. A class 'D' amplifier, which may also be known as a switching amplifier or a digital amplifier, utilizes output transistors which are either completely turned on or completely turned off (they're operating in switch mode). This means that when the transistors are conducting (switched on) there is virtually no voltage across the transistor and when there is a significant voltage across the transistor (switched off), there is no current flowing through the transistor. This is very similar to the operation of a switching power supply which is very efficient.