What does a brown spot on my white part of the eye mean?

Brown eyespots: Most spots on the whites of the eyes are due to pigmentary cells from embryonic development which produce such spots. These are common, have a much higher incidence in darker pigmented races, and are mostly benign. Rarely a spot might be a melanoma - watch for growth, discomfort and redness as clues to this.

Get it checked: It could be a nevus (benign freckle), a hyperpigmentation related to one's race, a tumor (melanoma). You must see an eye doctor.

A nevus: most of these are benign, but should be monitored for growth and / or increased pigmentation. surgical excision would then be recommended.