A semicolon is used to indicate a brief pause in a sentence; a semicolon tattoo is used to indicate a pause, and then a continuation, in a person's life.
Having a simple ; tattooed somewhere, most often on the wrist, often means that this person was at one point suicidal, but chose, metaphorically, to continue their sentence rather than end it. It is sometimes used more generally to help raise awareness of mental health issues and suicide prevention.