What function does a nystagmus have?

Not always: Nystagmus is the reaction of the eye to congenital low vision and optic nerve disease. It also occurs when the retinal vision is disturbed or too much light enters the eye. In these cases it might be a little protective to prevent burning the retina from outside light. Some of it simply occurs with no obvious pathology and in these cases the function is unknown.

No function: Is usually not desirable to have, and can be as a result of a congenital or acquired cause. Saccadic movements can appear as slow and fast, and might appear like it's nystagmus, when it's not, and are normal findings during testing.