The details are below; the bottom line is that in a class A amp, the output stage is on and passing current for both halves of the signal (+ and -). Consequently, during the time there is no signal, the devices dissipate power as heat. Class AB amps are designed so that there are devices dedicated to each half of the waveform so that less power is dissipated as heat and they're more efficient. The down side is that during the time the signal "crosses over" from + to - there may be a small delay in the device turn on that handles it and this cause a type of distortion known as cross over distortion. Many modern designs today work in class A up to a certain power level then switch to AB. Sorry for the verbose answer, but this isn't a simple topic.
Class A Amplifiers
Class A amplifiers operate over a relatively small portion of a tubes plate-current or a transistors collector-current range and have continuous plate- or collector-current flow throughout each RF cycle. Their efficiency in converting DC-source-power to RF-output-power is poor. DC source power that is not converted to radio frequency output power is dissipated as heat. However, in compensation, Class A amplifiers have greater input-to-output waveform linearity (lower output-signal distortion) than any other amplifier class. They are most commonly used in small-signal applications where linearity is more important than power efficiency, but also are sometimes used in large-signal applications where the need for extraordinarily high linearity outweighs cost and heat disadvantages associated with poor power efficiency.
Class AB Amplifiers
As the designation suggests, Class AB amplifiers are compromises between Class A and Class B operation. They are biased so plate- or collector-current flows less than 360 degrees, but more than 180 degrees, of each RF cycle. Any bias-point between those limits can be used, which provides a continuous selection-range extending from low-distortion, low-efficiency on one end to higher-distortion, higher-efficiency on the other.
Class AB amplifiers are widely used in SSB linear amplifier applications where low-distortion and high power-efficiency tend to both be very important. Push-pull Class AB amplifiers are especially attractive in SSB linear amplifier applications, because the greater linearity resulting from having one amplifier or the other always conducting makes it possible to bias push-pull Class AB amplifiers closer to the Class B end of the AB scale where the power-efficiency is higher. Alternatively, push-pull Class AB amplifiers can be biased far enough toward the highly-linear Class A end of the scale to make broadband operation without resonant tank circuits possible in applications where broadband operation or freedom from tuning is more important than power-efficiency.
Class A Amplifiers
Class A amplifiers operate over a relatively small portion of a tubes plate-current or a transistors collector-current range and have continuous plate- or collector-current flow throughout each RF cycle. Their efficiency in converting DC-source-power to RF-output-power is poor. DC source power that is not converted to radio frequency output power is dissipated as heat. However, in compensation, Class A amplifiers have greater input-to-output waveform linearity (lower output-signal distortion) than any other amplifier class. They are most commonly used in small-signal applications where linearity is more important than power efficiency, but also are sometimes used in large-signal applications where the need for extraordinarily high linearity outweighs cost and heat disadvantages associated with poor power efficiency.
Class AB Amplifiers
As the designation suggests, Class AB amplifiers are compromises between Class A and Class B operation. They are biased so plate- or collector-current flows less than 360 degrees, but more than 180 degrees, of each RF cycle. Any bias-point between those limits can be used, which provides a continuous selection-range extending from low-distortion, low-efficiency on one end to higher-distortion, higher-efficiency on the other.
Class AB amplifiers are widely used in SSB linear amplifier applications where low-distortion and high power-efficiency tend to both be very important. Push-pull Class AB amplifiers are especially attractive in SSB linear amplifier applications, because the greater linearity resulting from having one amplifier or the other always conducting makes it possible to bias push-pull Class AB amplifiers closer to the Class B end of the AB scale where the power-efficiency is higher. Alternatively, push-pull Class AB amplifiers can be biased far enough toward the highly-linear Class A end of the scale to make broadband operation without resonant tank circuits possible in applications where broadband operation or freedom from tuning is more important than power-efficiency.