A convex grind curves outward from the spine to the edge, so the blade’s cross-section bulges rather than tapering in a straight line. It puts the most steel of any grind directly behind the apex, which makes it the toughest.
A convex profile has no sharp transition anywhere. The steel thickens gradually and continuously behind the edge, so there is no thin section for a chip to start in and no shoulder for the blade to catch on.
That geometry also acts as a wedge, splitting wood apart as it enters. Axes, hatchets, machetes and heavy-duty knives all use convex edges for the same reason.
A flat stone naturally grinds a flat bevel, so it fights the convex shape. The traditional method is a leather strop loaded with compound, or a mousepad-and-sandpaper setup where the soft backing lets the abrasive wrap around the curve.
Maintained that way a convex edge is easy to keep going almost indefinitely. Taken to a flat stone often enough it becomes a flat grind by accident.