Explain Amp classes & how effects sound?

In terms of heat:

class A => hottest but otherwise the most linear/lowest distortion

class A2 (tubes only) grid current may flow in the tubes during part of the waveform but the tube is conducting through the entire wave cycle. This allows for more power but has greater requirements of the driver circuit.

class AB => less heat, slightly more power but slightly more distortion

class AB2 => (tubes only) similar idea to A2, but the tubes stop conducting through part of the waveform. You get a lot of power and a lot less heat, but crossover distortion is more pronounced.

Class C => not applicable to audio

Class D => so far, for practical applications so far is transistor only. The devices are either fully on or fully off, avoiding the much greater power requirements of operating the transistors in the linear region. This makes the most power with the least amount of heat. Distortion can be very high, but this is a developing field, and is likely the area with the most potential for improvement in the next ten years.

Most transistor amplifiers do operate pretty close to class B; at low power levels most of the power comes from the driver transistors rather than the outputs. But in order to keep the amplifier from making significant distortion (notch and crossover) at the zero crossing point, they have to have a certain minimum amount of bias current to make that happen. As a result they are considered class AB.