A Man-Bat was a human who had become animalistic and given "Bat-like" powers.
Via the Man-Bat Serum, Kirk Langstrom accidentally transformed deaf children into bat creatures. This compound was later stolen by Talia al Ghul and used by the League of Assassins in their endeavors. Al Ghul later used the same serum to power her own personal army in Leviathan. Al Ghul's use of the serum came to an end with the Battle of Gotham City.
The 900 Block of Gotham City was later subject to an airborne version of the serum, now a virus as it could spread from person to person. This problem was later solved by Kirk Langstrom himself, who made himself a Man-Bat to cure all those infected.