The term is a modern one, and is an acronym for beit din tzedek ("court of Justice").
In most Jewish communities, there has been a beit din, which was often headed by the rabbi of the city, hence the nickname "Rabbad" - combining "Rabbi" and "Av Beit Din."
In various ultra-Orthodox communities today, there are three jewish judges serving as a local badatz.
Badatz is not a major beth din according to the laws of the State of Israel.
Certain Badatz, such as that of the ultra-Orthodox community, do not recognize the authority of the State of Israel, and the judgments are not legally valid but only halakhic.