A "butterfly" nose is when a dog has patches of bright pink on its nose leather. These patches are randomly located and can cover any amount of the nose, from just a tiny pink spot to almost the whole nose. Butterfly noses sometimes occur on dogs with the extreme white spotting pattern ( e.g. white Boxers, Bull Terriers and Dogo Argentinos), but generally they're associated with merles. Not all merles have butterfly noses though -
Butterfly noses are created when parts of the nose have no pigment (the colour pink is associated with a lack of pigment). The merle gene dilutes random parts of the pigment on the coat and nose, creating grey areas on the coat and pink areas on the nose. Harlequin Great Danes have an extra gene which dilutes the grey areas on the merle to white, so this extra strong dilution means harlequins are highly likely to have a butterfly nose.