Many audio consoles have a switch indicated with the Greek letter, "φ" (phi). It is often, although incorrectly, referred to as the phase or phase invert switch.
However, what is really being inverted is the polarity of the signal. What this means is that the entire signal--all frequencies that make up the signal-- are inverted 180 degrees. What was a peak in the positive direction is now a peak in the negative direction.
A switch with the φ symbol should correctly be termed a polarity switch. It has the same effect as swapping the red (hi) and black (low) wires on a balanced audio connection (for example, swapping pins 2 and 3 on an XLR-3 connector).
If you put the same signal in two channels of your audio console, invert the polarity of one of the channels, then mix (sum) the two signals together at the same level, the audio level out of the console would drop to nothing. The out-of-polarity and the in-polarity signals would cancel each other out.
Another way to look at polarity and phase is that polarity is independent of frequency while phase is frequency dependent. When you talk about a phase shift of so many degrees, you need to specify at what frequency this happens.
True phase shifters, like flangers, are used for special effects and are often outboard devices when used with audio consoles, or plug-in software modules to digital audio workstations or editors.
