From Wikipedia.

Equilibrioception or sense of balance is one of the physiological senses. It allows humans and animals to walk without falling. Some animals are better in this than humans, for example allowing a cat (as a quadruped using its inner ear and tail) to walk on a thin fence. All forms of equilibrioception can be described as the detection of acceleration.

It is determined by the level of fluid properly called endolymph in the labyrinth - a complex set of tubing in the inner ear.

When the sense of balance is interrupted it causes dizziness, disorientation and nausea. Balance can be upset by Meniere's disease, an inner ear infection, by a bad common cold affecting the head or a number of other medical conditions. It can also be temporarily disturbed by rapid and vigorous movement, for example riding on a merry-go-round.

Most astronauts find that their sense of balance is impaired when in orbit, because they are in a constant state of free-fall while their rockets are off. This causes a form of motion sickness called space sickness.

Equilibrioception in many marine animals is done with an entirely different organ, the statocyst, which detects the position of tiny calcareous stones to determine which way is "up".