Class A amplifiers have no crossover distortion at the 0 point because they use a “single” device to handle a complete waveform. This structure is incredibly power consuming, heat creating, and low on efficiency (usually around 25%) and power (25-30W is an average ouput).
Class B amplifiers use two, or more, devices in a complementary pairing with the “top” one handling the positive half of the waveform and the “bottom” one handling the negative half. The two outputs are then summed to give you the complete waveform with the point that the waveform goes from positive to negative (and back) being called the crossover point. Because of the lack of perfect linearity between devices there will always be some distortion at the point of crossover. Class B amplifiers are usually used for high power work.
A class A/B amplifier uses a class A stage for low power work and then “switches” to the class B stage for higher power work.
See https://en.wikipedia.org/wiki/Power_amplifier_classes for help, too.