Twisted tail of wrapper left protruding from the head, also called a curly head. Traditional on Cuban culebras and lanceros, it is decorative and can be snapped off with the fingers rather than cut.
Why it matters
A pigtail signals a hand finish and gives you the option of tearing instead of cutting, which some smokers find opens a cleaner draw.
In context
"Twist the pigtail off, do not cut it, and the cap stays tight."