Western riding is a type of riding defined mainly by the saddle used. Western saddles have a horn, larger pommel (rise in the front of the saddle) and cantle (rise in the back of the saddle). There are many versions of a western saddle, but they all will have a horn.
Western movies are the most common depiction for someone riding western, though there are many disciplines in which people use a western saddle, including barrel racing, western dressage, western pleasure and trail.