A hawkbill blade curves downward like a talon, with the edge on the inside of the curve. It pulls material into the cut instead of pushing it away, which is why it is the standard shape for cutting rope, cordage, carpet and linoleum.
Hook the blade over a rope and pull. The curve traps the material at the base of the hook, so the more you pull the more the rope is drawn into the sharpest, most acute part of the edge. Nothing can slide off the front the way it can off a straight edge.
That same geometry is why hawkbills are used by roofers, gardeners and electricians. Pruning knives and linoleum knives are hawkbills under another name.
Push cutting is essentially impossible; there is no flat section to press. Board work is out. The point is also awkward to control because it faces down and away from your line of sight.
Sharpening needs a rod or the narrow edge of a stone, since a flat stone cannot reach inside the curve. See recurve blade for the related sharpening problem.