The half-angel half-devil tattoo symbolizes good and evil or good vs. evil. It is one of the many ways to symbolize this concept through body art.
How the tattoo is designed is primarily up to the preferences of the wearer, but it is typically a woman or man whose one half is the stereotypical angel and the other half the stereotypical devil, or demon.
This symbolism suggest an inner struggle and is often used by an individual who has felt the pull between good and evil, or light and darkness. Someone who has struggled through mental illness, for instance. There are other symbols that can be used for this dichotomy, such as yin-yang, which symbolizes light and darkness.