The carriage in Fable II is a way to fast travel from Oakfield, Westcliff, and Bowerstone Market to each other. In order to use the carriage, you must pay a fee for each ride. The upside to you using a carriage ride is that it is faster than your standard fast-travel or traveling on foot. The counterpart to the carriage is the ship which can be used to get to Westcliff or Bloodstone from each other.
Carriage Travel Times Modifier
The carriages' traveling times from place to place are different when you travel in different areas. The fees are changed as well depending on the distance from your location to the future area.