What does the following quote mean: "It is not what an author says, but what he or she whispers, that is important." and support 2 short stories.

What is unstated by the author is of more importance than what is overtly stated.  Afterall, most of the time, the reader must infer what the theme of a narrative is.  So, it is the suggestions of the various elements--setting, character, point of view, plot--that declare the most important message.

In Joseph Conrad's "The Secret Sharer," for example, the captain of a ship stows away in his own cabin a man who swims to his boat in the dark, a man whose physical appearance is much like his.  Even though he has broken the law by harboring a man who has admitted to murder, the captain continues to hide his "secret sharer" because of some immediate affinity that he feels for the other, referring to him as his "double," with whom "a mysterious communication was established immediately.  While never stating that the captain has sensed isolation before and now has meaning in his life from sharing it with another, Conrad has "whispered" this to his reader.

Likewise, in William Faulkner's "A Rose for Emily," the reader determines from the "whispered" inferences of character that Emily, who has become an anachronism in her town, seeks to rebuff the new world into which she is thrown by retaining as much of the old that she can.