Where is the spot located? Is it on the white of the eye? Or on the lid?
A brown spot on the white of the eye is most likely a mole (just like on the skin). If the lesion is getting larger, that would be cause for removing it (just like if it were on your skin). The only way to get rid of it is to remove it. Many times this can be done simply enough in the office.
Hope this helps and thank you.