In the context of physics, phase refers to the relative position of a feature (such as a peak or a trough) of a waveform, compared to that same feature on a second waveform. The phase may be measured as a time, distance, a fraction of the wavelength, or as an angle in radians.
Consider the two waves A and B in this diagram:
It's apparent that the positions of the peaks (X), troughs (Y) and zero-crossing points (Z) of both waves all coincide. The phase difference of the waves is thus zero, or, the waves are said to be in-phase.
If the two in-phase waves A and B are added together (for instance, if they are two light waves shining on the same spot), the result will be a third wave of the same wavelength as A and B, but with twice the amplitude. This is known as constructive interference.
Now consider waves A and C:
A and C are also of the same amplitude and wavelength. However, it can be seen that although the zero-crossing points (Y) are coincident between A and C, the positions of the peaks and troughs are reversed, that is and X on A becomes a Y on B, and vice versa. In this case, the two waves are said to be out-of-phase, or the phase difference of the two waves is π radians, or half the wavelength (λ/2).
Also consider waves A and D:
In this situation, a peak (X) on wave A becomes a zero-crossing point (Z) on B, a zero-point becomes a peak, and so on. The waves A and D can be said to be in quadrature, or exactly π/2, or λ/4 out of phase. This is the same relation that the mathematical functions sine(x) and cosine(x) have.
See also interferometer.