This is the initial phase of each ring, as a normalized angle. Setting this property rotates the entire pot around its center axis. If you just want to see the pot from a different angle, it's usually preferable to rotate the view instead, because doing so is very efficient, unlike rotating the pot which involves rebuilding the mesh.
This property is primarily intended as a modulation target, in order to achieve twisting effects by rotating each ring differently. The Twist property only supports simple linear twisting, whereas modulating Ring Phase allows many other types of twisting. The Twist property is equivalent to modulating Ring Phase with a unipolar Ramp Up waveform. Twist and Ring Phase modulation can also be combined for even more complex effects.