Refer to the attached drawing, which shows bottom views of the blade edges (i.e., turn your skates such that the top of the boot is pointed straight down and the blade edges are pointed straight up; and look down on the edges). The drawing is not to scale; certain features have been exaggerated to make them more visible.
(a) A standard Coronation Ace has a parallel edge geometry. The inside edge and the outside edge both have straight-line geometries; the sides of the blade are ground flat The inside edge is parallel to the outside edge along the entire length of the blade from toe to heel. The thickness of the blade is constant along the length of the blade.
(b) A parabolic Coronation Ace has a parabolic edge geometry. The inside edge and the outside edge both have curved-line geometries; the sides of the blade are side-honed concave [the side-honing by itself yields different edge properties than those of the standard Coronation Ace, but I won't go into those details]. The thickness of the blade is greater at the toe and the heel than at the center of the blade. If the blade is ground with a constant radius of hollow (ROH), the bite angle of the edges depend on the thickness of the blade: the edges have more bite at the toe and the heel than at the center. Since glides are done near the center of the blade, less bite gives smoother glides. Since turns are done near the toe or the heel of the blade, and spins and jumps are done near the toe of the blade, more bite gives better control. Anyway, that's how it works in theory. But since the Coronation Ace is an intermediate blade, I don't think it's worth it; though I personally have not tried a parabolic blade myself. Also note that it's difficult to check the quality of sharpening (depth of hollow and evenness of edges) for a parabolic blade.