Terms like 'audio channels' can sound confusing, especially when looking at a huge mixer with hundreds of knobs. But perhaps an illustration from the real world will help.
What do we call a channel in the real world? It could be a canal that transports water from a lake to a distant location. A distribution channel, is a method of distributing a product to customers. Essentially, a channel is a path to transmit something from one point to another. And it's the same type of concept with audio channels. Except now you're transmitting sound.
The concept of a channel involves, well, creating a separate path of sound for each instrument. Why do that? Because when different instruments are routed through different channels, you could apply different effects to each instrument. If there were no channels, and sounds from all instruments were routed through the same path, it would be impossible to create a good sounding mix. Each instrument needs its own set of effects to get it to sound right.
So when you look at a huge mixer at a church or concert hall, it may look like a lot of knobs. But if you look closer, you will notice that most knobs are repeated in a pattern, column after column. Those columns are used for each individual channel.
When you an instrument to one of these columns, you could modify the sound coming from that instrument using the knobs on the mixer board.
A physical mixer board has only the basic effects that can be applied to the channels. A software mixer can have much more effects.