Black Cat tattoo designs are usually associated as a symbol of the Occult, Witches and Pagan religions. During the terrible times of the Medieval Inquisitions carried out by the Roman Catholic Church, individuals who were thought to be heretics or witches were actively sought out.
In Medieval Europe during the Middle Ages, women often had knowledge of medicinal herbs and remedies and they were objects of some suspicion by the male-dominated church. The image of a Witch at a cauldron mixing a magic potion comes from nothing more harmless than a woman, usually a crone past her child-bearing years, gathering herbs and medicinal plants in the forest and creating folk-medicine for members of her family or village. Heresy!
Black Cats were thought to be "familars", or companions of witches and that was often enough reason for a woman to be accused of being a witch. In a period that has been called the "Dark Ages" for good reason, black cats were seen as demons in disguise and creatures under the power of Satan. It did not help the case for cats, that despite their abilities to keep vermin in control, this was also the period of the Crusades and in the Middle East and Egypt cats were revered.
The Black Cat as a tattoo design may symbolize a belief in feminism, independence from male domination, or an admiration for Pagan or Wiccan spiritual beliefs.
A variation of the Black Cat tattoo design, is the Black Panther that is the symbol for X-Rated or Restricted movies, meaning that the films in question contain graphic nudity and/or sexual situations which are deemed unsuitable for minors.
So there is also a strong element of the erotic, sensual and sexual in the Black Cat or Black Panther tattoo.
