An exposition is "one of four rhetorical modes of discourse, along with argumentation, description, and narration. The purpose of exposition is to inform, explain, analyze, or define." - Wikipedia
In my opinion, Exposition essentially means explanation. Exposition explains and informs the reader of a certain subject or idea. Expositions are also referred to as expository essays; like any other essay, expositions require clarity, strong organization, listing of events in chronological order and above all, focus. Digressing would be a serious fault. To me, this would mean that the writer has to have plenty of knowledge over the subject he would write on.
Also, exposition is all around us, from books, magazines, newspapers to school exams, research papers and even work reports. This makes me feel miniature in the huge library of knowledge out there in which people are browsing books from, learning in the process. I hope that I too, will eventually be able to write good expositions.