Tufte's best example of layering and separation is the comparison of maps on pg. 58.
He explains that when elements of a map/representation/etc are "at the same visual level with equal values, equal texture, equal color, and even nearly equal shape"...."an undifferentiated, unlayered surface results."
This quote demonstrates the results of a lack of layering and separation. Differentiation is necessary to avoid jumbling information and causing the message to disappear among the clutter.