Essays are potentially the greatest literary form. Three things are necessary to make an excellent essay: an idea, economy of language, and an engaging style. You don't have long to get the reader on your side in an essay, so you'd better try from the beginning. Some of the best writers have spent most of their careers writing essays, and they continue to make some of the best reading and some of the best texts for teaching writing.
The poorly executed essay, on the other hand, can make for some of the most arduous reading imaginable. Ralph Waldo Emerson may have been one of the first truly American intellectuals, and he certainly helped found one of the new nation's greatest literary movements (Transcendentalism), but his essays are mere soups of words, jumbled thoughts expressing only the idea that clarity of thought or expression is impossible. If you think this is an exaggeration, consider a statement by the diminutive New Englander: "Consistency is the hobgoblin of small minds."
A capable writer like Twain, however, understood the power of the short work. As his essays exemplified, you don't start or end vaguely; to capture the reader's imagination and affect his thoughts, you begin in familiar territory, lead him through unfamiliar places, and conclude by showing how what was unfamiliar is now recognizable.
To do this repeatedly without merely treading the same few steps over and over takes a brilliant writer. One of the ablest modern practitioners of the essay is Annie Dillard, many of whose books are simply collections of shorter works. Her poetic vision lights little fires on the page, which when read become full blazes. Yet her effect isn't destructive; Dillard unites the elegance of language with the primitive terror of nature and the holy in ways that make us see the beauty of both in new ways.
Letters are often just personal essays. One of the exchanges one makes for greatness is the right to postmortem privacy, and we read the letters of people like Heloise and Abelard, Thomas Jefferson, and Winston Churchill to discover the secret of their greatness. What we usually find is the one universal feature of great writers—a vigorous and well-organized mind.
This is the secret of good writing, after all: the ability to think plainly and translate those thoughts to the page. Essays and letters (when done well) illuminate this skill largely because of their brevity (unless you're Kafka writing to your parents). There's no time to get lost when the path is short, and even less when that path is lit by eloquence and wit. If you write and you want to get better, read some good essays and imitate what you find.