Which body part keeps you balanced?

The inner ear - specifically the vestibular system, three fluid-filled semicircular canals set at right angles to each other, plus two chambers containing crystals resting on hair cells. Between them they detect rotation in any plane and linear acceleration including gravity, which is a complete inertial navigation unit built into your skull.

It works by inertia: when your head turns, the fluid lags, bending hairs that fire nerve signals. This is also why spinning makes you dizzy. The fluid catches up while you are spinning, so when you stop it keeps moving, and the system reports rotation that is not happening.

Motion sickness is thought to be the same mismatch. Below deck on a ship or reading in a car, your inner ear reports motion and your eyes report a stationary room, and one influential theory holds that the brain treats that specific contradiction as a symptom of poisoning - since neurotoxins disrupt sensory integration - and responds by inducing vomiting. It is a plausible account of an otherwise pointless misery, and it explains why VR headsets can do it to a person sitting perfectly still.