What does Vaulting mean?

Answer 1

Jumping, but it implies that it was either very high or very far. Or it is a term used when you try and jump onto a horse without using stirrups or a block

Equestrian Vaulting is a unique and growing sport that combines gymnastics and dance on a moving horse. It's a wonderful way to develop coordination, balance, strength, and creativity while working in harmony with your equine partner. If you love horses, gymnastics, dance and fun.

Is it like trick riding or circus riding?

No. Vaulting is always done in a very controlled environment-in a fully enclosed arena in a consistent, large circle, in soft footing, with the horse attached to a "lounge" line and controlled by a trainer (called a longueur). The horse, longueur and vaulter work as a team, with the longueur controlling the horse, the horse performing at a continuous gait (either walk, trot or canter, depending on the vaulter level). The vaulter performs a series of gymnastics and dance moves on the horse as it moves in its circle.