This somewhat unflattering name refers to the quarter-rounding or half-rounding of the edge of the coping, so that it provides a smooth, soft, and safe edge for swimmers. The bull nose concept is also sometimes applied to steps, ledges, and other Hardscapes surfaces.
Most precast coping (such as brick or cement) is manufactured with the bull-nose feature built-in. With natural stone, the installer has to hand carve the bull-nose on site; thus the phrase hand-carved bull nose.