Hannya is a masked man who wears a weird outfit with red and black stripes on the sleeves, which have some sort of illusion. This illusion is that the stripes, when a punch is thrown, become vertical and to the mind condense distances (making Hannya's arm seem longer than it actually was). This effect, much like a telephoto lens distortion, was quite effective on Kenshin's depth perception until he used his sword like a temporary measuring stick.
Hannya was born in a poor village which had famine for years. His parents tried to kill him when he was still a child in order to lessen the number of family members they had to feed. Somehow, he managed to escape and was forced to live in the wild, fighting with animals for food until he was picked up by Aoshi. Aoshi trained him to become one of the best Oniwabanshuu warriors. In order to become Aoshi's right-hand man, he even disfigured his face so that he could easily disguise himself as anyone.
In Japanese lore, the hannya mask is specifically used to represent a vengeful and jealous woman. Her anger and envy have so consumed her that she has turned into a demon, but with some important traces of humanity left.