Is Equestrianism related to riding on a horse back?
That is exactly what it is! Equestrianism is know as riding, horse riding, or horseback riding. This can even include vaulting with horses. 
What do you mean by the term vaulting ?
vaulting is gymnastics and dance on horseback. This can be done in competitions. Also in competitions is rodeo, horse racing and even polo.
 Is it an olympic event?
Olympic Games
The modern Olympic Games or Olympics () are leading international sporting events featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a variety of competitions. The Olympic Games are considered the world's foremost sports competition with more than 200 nations participating. The Olympic Games are held every four years, with the Summer and Winter Games alternating by occurring every four years but two years apart.
Their creation was inspired by the ancient Olympic Games, which were held in Olympia, Greece
Equestrianism
Equestrianism (from Latin , , , 'horseman', 'horse'), more often known as horse riding (British English) or horseback riding (American English), refers to the skill and sport of riding, driving, steeplechasing or vaulting with horses. This broad description includes the use of horses for practical working purposes, transportation, recreational activities, artistic or cultural exercises, and competitive sport.
Overview of equestrian activities.
Horses are trained and ridden for practical working purposes, such as in