A statue is a sculpture depicting a specific entity, usually a person, event, animal or object. Its primary concern is representational. However, as with all artistic topics, this definition of the concept Statue is far from exhaustive and can be/needs to be expanded.
Many statues are built on commission to commemorate a historical event, such as the Battle of Iwo Jima, or the life of an influential person, such as Mahatma Gandhi. Many statues are intended as public art, exhibited outdoors or in public buildings for the edification of passers-by.
An urban legend concerning a code for mounted statues, whereby the horse's hooves are supposed to indicate how the rider met his end, is not true. 
A small statue is defined as being a statuette.