The most significant thing an author can convey through the use of stereotypes is that the stereotypes leave quite a bit out. When a writer presents a group stereotypically, he/she can express 1) a generalized perception of this group and 2) ways in which this perception is accurate and ways in which it is flawed.
Stereotypes in literature can be used in a wide variety of ways, as some of the previous answers have already suggested. Stereotypes can be reinforced and/or undercut. They can be used as sources of comedy and/or tragedy. They can be used to affirm people and/or to denigrate people. Much depends, then, on precisely what an author is trying to accomplish in any given work. Stereotypes are often simple, predictable, and unsophisticated, and works using stereotypes are often considered unsubtle, uninventive, and inartistic. On the other hand, many of the greatest works in world literature employ "archetypes" (such as the hero, the villain, the friend, the mother, the father, the sibling, etc.), and much of the powerful impact of such works often depends on the ways writers manipulate, alter, affirm, and/or complicate such "typical" characters.
The use of stereotypes create the greatest relation for a reader when an author uses the stereotype and the reader agrees with the characterization. Unfortunately, some readers who do agree with the stereotype will fail to relate or engage with the text if a frivolous stereotype is given.
Typically, an author can make any stereotype characterization based upon the fact that the majority of people feed into, or believe, the stereotype.
Typically, an author is reliant on the fact the the stereotype exists. If the stereotype fails to exist, a reader fails to identify the character through known characteristics.
Stock characters are often used, particularly in short stories, because they convey something big in just a few words. For example, saying someone is a "man of military bearing" draws a quick picture (uses only a few words) from which we can envision a character. (Works the same for a typical cheerleader, nerd, model, athlete, grandmother, butler, among other things.) A great example of this is Ivan in "The Most Dangerous Game." Stock characters are neither round nor static, of course, and they are rarely the primary players in a story; however, they generally add color and texture to any narrative.
Sometimes, as in postcolonial literature, using stereotypes is a means of attempting to deflate the authenticity of the stereotype thus reducing or eliminating their power and reality. This may be seen in Edwidge Danticat's work.
Stereotypes are often stock characters who serve in comedies for comic relief as they are recognizable to audience. For instance, a parody of the stingy Scot or who drives a hard bargain can easily bring laughter to a comedic play. (To some extent, for instance, the television show Seinfield employed a Jewish stereotype with George.)
The plot of the trial of Tom Robinson points to the stereotyping of Tom in Harper Lee's To Kill a Mockingbird. In this novel, the author attempts to break down stereotyping, as does Mark Twain in his The Adventures of Huckleberry Finn. The Reverend Mr. Wilson is the sterotypical Puritan minister in The Scarlet Letter, and such, represents the sanctimonious Puritan whom Hawthorne criticizes in his novel.
If an author agrees with a stereotype and wants to perpetuate it, use of the stereotype may simplify the presentation of the characters or the motivation behind their actions. If an author is presenting the case against a given stereotype, the story may need to be more carefully written to illustrate situations or actions that break down the expectations set by the stereotype. Showing the exceptions to the common mindset can take extra planning, but can be an effective way to counteract stereotypical impressions.