The central purpose of an expository essay is to explain an issue, advance an argument or pursue an investigation. Its paramount virtue is clarity. A good example of an expository essay is an encyclopedia entry, the purpose of which is to convey a simple and direct account of some subject previously foreign to the reader. The expository essay is primarily a teaching instrument, meant to edify, rather than persuade. Typically, it is preoccupied with the presentation of evidence to bolster the explanation it provides.
One way to develop a pertinent title is to think of it as an introduction to the content that follows. In this case, the title is used to concisely convey a snapshot of the essay’s principal theme. For example, novelist Elizabeth Hardwick wrote an essay for “Harper’s Magazine” on the deteriorating quality of book reviews written in America. She simply entitled it, “The Decline of Book Reviewing.” At a quick glance, the reader knows that the essay will propound an argument and has a fair idea of the basic substance of that argument.
Sometimes the best title is one that might not be all that informative, but firmly grabs the reader's interest because it is so unusual. For example, an essay on professional auto racing could be entitled "Mortality on Wheels" or an chef's memoir could be called "The Jagged Knife and the Silver Spoon." In both cases, the title only obliquely hints at the content. However, they're both intriguing enough to potentially inspire a reader to continue on.
Incomplete titles perform both the function of the informative and seductive versions; they give the reader some sense of the content, but only obliquely. They can also be intentionally provocative. For example, essayist Joseph Epstein wrote a short biographical article on the artist Susan Sontag, entitled, “A Very Public Intellectual.” In this instance, the title is a bit vague, though it does impart some sense of the subject matter. The reader knows it’s about a famous intellectual and the title hints subtly that the intellectual in question is going to be criticized for being too public, maybe excessively craving attention. Since the title only incompletely informs the reader what the article is about, it entices him or her to read on.