Basically the opposite of an anti-hero. While the anti-hero often fights on the protagonist's team, but with selfish motives, the anti-villain plays a villain's game, but for what's at least in their eyes a noble cause. They may be personally more noble or heroic than an anti-hero but the means to achieve their ends are often considered immoral, unjust, even evil. Sometimes they may simply be a villain with gentlemanly qualities or a code of honor or some sense of justice. Anti-villains will occasionally side with their rivals (usually the protagonist) if a greater threat than themselves comes or it is in both of their best interests. Often also considered "grey" characters due to their moral ambiguity.
In comparison, a Character who has villainous qualities (poor attitude, no morals, no respect for personal rights, etc.) but ultimately seeks heroic agendas or goals would be considered an Anti-Hero instead of an Anti-Villain.