I’m pretty sure that channels just represent speakers. So 2 channels, means you can hook up 2 speakers. 4 channels, 4 speakers & so on.
As for classes.. if it’s an analog…
Class A
The amplifier conducts current throughout the entire cycle (360º). The Class A design is the most inefficient and is used in low-power applications as well as in very high-end stereo. Such devices may be as little as 15% efficient, with 85% of the energy wasted as heat.
Class B
The current flows only 180º for half the cycle, or two transistors can be used in a push-pull fashion, each one operating for 180º. More efficient than Class A, it is typically used in low-end products.
Class AB
Combines Class A and B and current flows for 180º to 200º. Class AB designs are the most widely used for audio applications. Class AB amplifiers are typically about 50% efficient.
Class C
Operating for less than half of one wave cycle (100º to 150º), Class C amplifiers are the most efficient, but not used for audio applications because of their excessive distortion.
Class G
A variation of the Class AB design that improves efficiency by switching to different fixed voltages as the signal approaches them.
Class H
An enhancement of the Class G amplifier in which the power supply voltage is modulated and always slightly higher than the input signal.
If it’s digital..
Class D is a digital-like amplifier that works by turning a transistor fully on or off, but the “D” technically does not stand for digital. See Class D amplifier.
Class T
A variation of the Class D technique from Tripath. Class T modulates the pulses based on the individual characteristics of the output transistors.