Originally drawn by just two horses, with a coachman, the passengers were kept nice and safe (hopefully warm and dry too), in their enclosed carriage. It wasn't the most comfortable of journeys, with only leather bound attachments. Thankfully in 1754 steel springs were being introduced. Which improved it somewhat.
Carriages with four horses were called a coach and four, whilst six horse carriages were introduced in 1619. Both would feature a postilion (someone who rides & guides the horses from the front).
Carriages were a luxury item, with some not so 'special' shall we say, for the general public's use. From here they were altered to carry goods and merchandise, as well as being used for the police and fire departments. Name and brands would decorate the sides, so as not to be confused with transport.
Today they are classed as yesteryears vehicles, as we speed along in our warm, smooth riding cars, buses, lorries and so forth. Some are still privately owned with the Royal Family bringing theirs out for special occasions.