A vampire's master is the older vampire by whom he or she was brought across. The term "master" in this sense is not peculiar to the Forever Knight universe, but is quite commonly employed in modern vampire fiction in all media.
The implications of the term "master" are discussed in the episode "Killer Instinct", where LaCroix avers that, although he is Nick's master, that does not make Nick his slave. Certainly, although there are vampire masters—LaCroix among them—who do keep at least some of the vampires they create in a sort of family, there is no compulsion upon their "children" either to live with them or to obey them. Nick frequently does things of which LaCroix disapproves; and LaCroix can only attempt to prevent or dissuade him.
Several Forever Knight episodes strongly suggest that there is a permanent bond between a vampire and his or her master, allowing them to sense each other's whereabouts. The precise nature of this bond has been variously interpreted by fans.