The mute button is one of the most basic functions of an audio console. When the mute button is engaged the track is not audible (or muted). If the button is disengaged, the track is on and audible. If you don't see a 'mute' button on your console, you may simply have a track on/off button or switch. When the track is in the 'on' position, the channel is essentially unmuted, and when the track is in the 'off' position, the channel is essentially muted,
When automation was just a dream, the mute button was first on the wishlist. Mute was the first feature on consoles to be automated. Think about the ability to have tracks automatically turn on and off in syncronization with a project. It something that we take for granted now, but was a big deal and a powerful tool not too long ago.
Most DAWs have the option of muting individual audio regions within a track. This lets you keep your regions in place, while being able to mute certain parts to maybe try out a new arrangement bring elements of a looped project in and out.