Hannya tattoos are iconic, as is the story behind the demon itself. Although they began as humans, the folklore legend goes that the women who become these angry ghosts were usually spurned by a lover, and their jealousy, hate, and anger turned them into the Hannya demon. The infamous face comes from Noh theatre, a form of theatrics that includes the use of masks, dance, and music. The masks that Noh actors use to play the part of a Hannya in a play include the archetypal horns, fangs, and angry, but forlorn eyes that are now an integral part of the aesthetics of Hannya tattoos.
While "Noh" means "skill" or "talent", "Hannya" means "Wisdom" in Buddhism. Now, hopefully you realize that being full of jealousy and anger isn't the most wise way to live your life, but people usually explain that the name Hannya mask can be traced back to a famous Noh mask carver, Hannyabou, who lived in the 15th or early 16th century. Perhaps people get Hannya tattoos to remind themselves of the girl they screwed over, or maybe to remind themselves not to become a super angry demon. Or maybe it's because they look so damn cool.
One of the most well known stories about Hannya's is about a samurai named Watanabe no Tsuna. The tale goes that a Hannya who was tormenting travelers who passed through the Rashomon gate in Kyoto. When the samurai Watanabe came forward to kill her however, she changed into a beautiful woman and asked Watanabe for a walk home. The samurai agreed, but once he looked over his shoulder he saw the lovely woman change into the demonic Hannya and chopped off her arm. While most people get Hannya tattoos that only show the mask, some people have gotten entire stories covering their bodies...this is how Irezumi usually works. Your body tells the legends of Japanese heroes and demons!