The anti-villain is the converse of the anti-hero
(i.e., an individual who pursues a noble goal, though often employs ignoble means to reach it). As such, the anti-villain pursues undeniably villanous goals, but employs arguably noble methods to achieve them. Ultimately, it's the primary motivation that differentiates the anti-hero from the anti-villain.
True anti-villains are a rare occurance in literature and film. Often anti-heroes and/or accidental villains (i.e., people who pursue noble goals with unintended harmful consequences) are mistakingly identified as anti-villains.
Detective Vic Mackey from the television series "The Shield" is a corrupt policeman who seeks to illegally enrich his own life, though does so by way of incarcerating or exposing other criminals. As such, Detective Mackey serves as an archetypical anti-villain.