a two-wheeled, one horse carriage often let out for hire
The development of modern taxicabs closely parallels that automobile.
Originally selected owing to yellow's high visibility and common in horsedrawn form in Paris and London in the 1800s and New York in the 1880s. Now chiefly associated with the yellow automotive taxicabs popularized around New York by the Yellow Taxicab Co.
余談:
In reference to sexually available Asian women, a calque of Japaneseイエローキャブ (ier kyabu), from Englishyellow cab and popularized by Shko Ieda's 1991 novel by that name, from its female characters' supposed "yellow" skin and the notion they provided "rides" to the general public.