The line out phase switch is important when playing on stage through both your own cabs ánd the front of house.
The phase of a signal determines it’s timing. Depending on a lot of variables in the signal path to both your cabinets and the FOH mixing console, the timing for one of them can be ‘out of phase’. Two signals that are out of phase tend to cancel each other out. In this case, resulting in a very loose, vague and muddy sound for the audience. Switching the line out phase selector eliminates this problem.