In the 19th Century a "Hack" was a horse & a "Hackney Man" was the man who rented out these horses. The term was derived from Hackney Horses which was a particular breed. Individuals would rent a hack/horse that they could then ride themselves to their destination.
A livery also often provided hacks, but also offered rides much like a taxi or chauffeur, as well as often boarding & caring for other peoples horses for a fee.
Amylynne (Baker) Murphy