The overall meaning of the three is to suggest that the emperor shall not bathe in the wealth he possess and neglect the voice of his suffering people.
As mentioned in @huotuichang's comment below, this phrase does not only apply to emperors, although it might have originally been used to refer to emperors.
I'll explain each with their literal translation and connotation.
"Five colors blind your eyes."
Five colors refer to the treasures and jewelries. The various colors of luxuries shine to blind the eyes.
"Five notes make one deaf."
Five notes refer to the pleasing music pieces. While one enjoys the melodies being played, he is not able to hear the crying of his people.
"Five flavors make one loses taste."
Five flavors refer to the tasteful foods and drinks. 口爽 means losing one's taste. If one eats such foods daily, he will eventually lose his taste and will not be able to swallow the foods of the poor.