Phase denotes a particular point in the cycle of a waveform, measured as an angle in degrees or radians. It is normally not an audible characteristic of a single wave (but can be when we use very low-frequency waves as controls in synthesis). Phase is a very important factor in the interaction of one wave with another, either acoustically or electronically.
The video example below traces a sine wave by plotting the height of the tip of a spoke (or radius) of a rotating wheel (y-axis) against time (x-axis). The height of the spoke-tip corresponds to the waveform's relative amplitude, here plotted between an imaginary +1 to -1. To measure the phase angle in degrees, we start with the reference of the spoke pointing completely to the right and refer to that as 0º, with a relative height or amplitude of 0 as well. As the wheel rotates counterclockwise, the sine wave reaches its peak positive amplitude when the spoke has traveled 90º from its starting point (click on the image to start and stop), with a relative amplitude of +1. At 180º from the starting point, the amplitude of the sine wave has returned to 0 . At 270º, the sine wave reaches its peak negative amplitude of -1 and then returns to 0 as it returns to its starting point of 360º or 0º. As demonstrated on the frequency page, phase angle can also be measured in radians, with 2π radians being the equivalent of 360º, a full cycle or rotation of the wheel.
Another common sinusoidal waveform used in synthesis or measurement is the cosine wave, which is exactly the same shape as a sine wave and would sound exactly the same all by itself, but is distinguished by the fact that its cycle begins 90° out of phase to a sine wave, or at +1.