The term means face to face in French. It is also the term used for a carriage built in the 19th century, originating in France, where the passengers sat face to face. In America these carriages found their way into Urban areas. They weren't as useful in the country or on the farms. They needed well developed roads for the type of wheels and suspension. Farm and country roads were rough and rugged and needed a different type of wheel and suspension for their wagons and carriages. Here is a link to Carolina Carriages with a Vis-a-vis you could hire today. In the later part of the 19th century they often sat up to 6 passengers plus the driver and for an extra seat one could sit next to the driver. However in the earlier part of the century they were a narrow carriage and could only sit two. The advantage to this was the passengers weren't jolted against one another and it tended to be warmer than larger coaches. It fell out of fashion for a few years around the mid-century then the reconstructed ones were larger and interest in them gained once again.
It's a great carriage to use in an Urban setting.