Phase describes where in its cycle a periodic waveform is at any given time.
The relationship in time of two or more waveforms with the same or harmonically related periods gives us a measurement of their phase difference.  Phase cancellation occurs when two signals of the same frequency are out of phase with each other resulting in either a boost or cut in the overall level of the combined signal. 
Phase and Phase difference is a real-world issue in areas such as electrical wiring of audio equipment, signal path, and microphone placement during the recording process. Phase reversal can be a serious compromise of sound quality or a special effect affecting the perceived spaciousness of the sound depending on the context of its ocurrence.  For frequencies that are harmonically related a constant phase difference will result in a different waveform but this difference will not be detected by the ear. 
Consider the following example where two simple tones of different frequency are added together. In the first case we start with the two tones, a fundamental and first harmonic, in phase as diagrammed below:  The following diagram illustrates the resulting waveform after these two in-phase frequencies are added together: 
Now consider the following situation where the same two frequencies are added together with the second one out of phase by 90 degrees as illustrated below:  The following diagram shows the waveform resulting from the addition of these two: 
Although a different waveform has resulted due to the phase difference, this combination of frequencies will sound the same as the first, in-phase combination.