The dizziness you experience when you spin is caused by the fluid in your inner ear, called endolymph, moving around. Your inner ear is responsible for balance, and it contains three semicircular canals that are filled with endolymph. When you spin, the endolymph moves around and pushes on the hairs inside the canals. This sends signals to your brain that you are spinning, even if you have stopped. Your brain then tries to correct for this by moving your eyes and body in the opposite direction, which can make you feel dizzy.
The dizziness you experience when you spin is usually temporary and will go away after a few minutes. However, if you have chronic dizziness, it is important to see a doctor to rule out any underlying medical conditions.