In common language, it is an unlawful act punishable by a state or other authority.
In Criminal Law, the definition is not the same everywhere.
A common definition is that a crime or criminal offence is an act harmful not only to some individual, but also to a community, society or the state (i.e. a “public wrong”).
e.g. Murder, Rape, Theft
Usually, to be classified as a crime, the “act of doing something criminal” (actus reus) must, with certain exceptions (Strict Liability), be accompanied by the “intention to do something criminal” (mens rea).