The Black Bat is a heroic persona donned by Cassandra Cain following her relocation to Hong Kong.
Due to his influence and her previous time as Batgirl in Gotham City, it is presumed that the Black Bat persona in Hong Kong is similar to the persona of the Batman in Gotham City; a dark "bat-like" spectre who preys on the guilty and corrupt in the city and protects the city's victims and innocents.
Following Bruce Wayne's "death" during the Final Crisis, Cassandra Cain obeyed his last will and testament and passed the mantle of Batgirl to her friend, Stephanie Brown.
Now without a mantle, her father figure and commander dead and her adopted family in disarray, Cassandra traveled to Hong Kong, presumably also due to Bruce's last will and testament, to start afresh.
Still not wishing to be the assassin her father wished her to be but also believing that she could no longer be a Batgirl due to Stephanie now possessing the role, Cassandra was directionless for a period of time; eventually donning a vigilante costume and continuing protecting people in Hong Kong as she had done in Gotham.
It wasn't until Timothy Drake visited her and gave her a copy of her old Batgirl suit, with the offer to return to Gotham as Bruce had returned and was restablishing the family, that she took up the Bat symbol again and came to be known in Hong Kong as the "Black Bat".
Recruited by Bruce as the Hong Kong agent of Batman Incorporated, Cassandra kept watch on various corporate and street-level crime in the city. This included international shippings and in doing so she briefly returned to Gotham in pursuit of a shipment of explosives heading towards the city and assisted her step-brothers in saving the city from a vandictive relative of one of the city's historic architects.