Vault is a verb that means "to jump over something." If you were hurrying out to the pasture to visit your favorite cow, you might vault over the gate in your excitement.
When you support yourself with your hands as you jump over some hurdle, you vault, just as a gymnast might do across a vault — a piece of gymnastic equipment made to be vaulted over after a running start. Another meaning of vault is the arched roof of a building, or something that resembles such an archway. A storage chamber, especially one that's kept underground, is also a vault, like a bank vault.