A v cut (cat’s eye) punches a wedge rather than a flat slice. The opening is smaller than a full guillotine cut and can concentrate the smoke. Some people prefer it on smaller rings and on pointed belicosos; some dislike it because the notch can collect tar or split a dry cap.
It is still a cut of the cap, not a different cigar. If the V is off-center or too deep, you have the same unwrapping problem as a bad straight cut.
See punch for a hole instead of a wedge, and cutter for the family.