Something with layers of meaning has
depth. Although
obvious to understand, the property of having layers of meaning is not easily noticed.
Brain-Spraining Books have layers of meaning, and it is for this reason that they are
worth reading - they expand one's
intellect.
To demonstrate layers of meaning, examine a book. On one layer of meaning, it is a collection of dots. On another, it is a collection of symbols. And on another, it is a collection of words. However, it has another set of layers of meaning - those contained in its words. These may be mutually exclusive or supporting. Some may only be visible from certain points of view.
Generally, it takes more than one reading to understand layers of meaning.
See: Gödel, Escher, Bach. This Great Book is entirely about this. At least, on one layer of meaning, it is.