I've always thought the significance of a spiral form lay in the way it graphically connotes both cycles and infinity.
A spiral motif is the simplest way to create an arbitrarily elaborate figure by merely repeating the same elementary shape over and over (at different scales). This naturally connotes repetition or cycling.
A spiral figure is also the only motif that affords the ability to extend a continuous line to the limits of feasible representation, because you can extend the spiral's line inward / smaller or outward / larger as far as you can draw (carve, etc.). This implies infinitude.