Symbols are techniques authors use to provide a rich undercurrent to their theme and message. Symbols can express deeper meaning and richer import than straight explanations can because of the images symbols and associations evoke. For example, the Alps evoke strong images of might, loftiness, purity, freedom, so a heroine who regularly wears a necklace with a pendant shaped as part of the Alps will be strongly associated with the qualities ascribed to the Alpine Mountains. Therefore, Salinger used symbols in order to give a deeper, richer fabric of understanding to Holden's struggle with growing up.
The use of symbols can be rather frustrating for those that are perhaps unused to identifying and exploring how symbolism adds greatly to the meaning of a novel or text. However, symbols allow authors to suggest many different layers of meaning, or to indicate possibilities that clearly making a simple, literal statement could not achieve. Many critics liken symbols to a pebble that is thrown into an absolutely still and calm pond, with the many ripples spreading out from where the pebble hits the pond representing the many layers of implicit meaning.
Note for example the symbol of the Museum of Natural History. Holden is drawn to the exhibitions of the Mummies and the Egyptian tombs because of the way that "it is nice and peaceful" and the way that the mummies present an image of frozen time. Note what Holden says to the two kids that ask him where the mummies are:
"They wrapped their faces up in these cloths that were treated with some secret chemical. That way they could be buried in their tombs for thousands of yearsand their faces wouldn't rot or anything. Nobody knows how to do it except the Egyptians. Not even modern science."
Clearly, what draws Holden to the mummies is the way that they represent something that he desperately desires: to be frozen in time and not to grow any older. He finds the tomb peaceful because it helps him believe in his fantasy world where everything stays the same, nobody has to grow up and things are understandable and trapped in some kind of stasis. To Holden, therefore, the genius of the Egyptians is massive. Their technology in preserving and trapping time makes them more advanced than "modern science," which seems to offer him no hope of avoiding growing up and the confusing state of affairs that this is. However, the author doesn't go out and say all of this. He leaves us to work it out, making the meaning of this symbol far more powerful than if he had stated it directly.