What does it mean when the background of your eye is yellow looking?

Depends: The normally white part of the eye turns yellow due to increase in bilirubin (a breakdown product of hemoglobin metabolism) which stain the conjunctiva (membrane covering the white of the eye). This is most commonly related to liver disease and should prompt a visit to the doctor.

It might be Jaundice: If you mean that the white of your eye has some small yellowish areas beside the colored tissue of the iris, that could be a 'normal' change called pengueculum. If you mean that the whole white of the eye is distinctly yellow, the liver may be letting bile pigment, bilirubin, in the blood, staining the white of the eye (jaundice). Liver problems that severe require exact diagnois and treatment.