Style refers to the mechanics and conventions of writing, and to the over-all quality or tone of a written work. When we begin a new novel, it is our response to the style that usually determines whether or not we continue to read it (unless it is required reading, of course).
Most of us have discarded a book after the first chapter, too early to have a comprehensive sense of the content of the book. The tone of the book does not appeal to us, so we turn to something else. Potential employers and instructors do the same to a greater or lesser degree: an employment manager may not read a messy resume to discover your excellent qualifications, and an instructor may not be receptive to your arguments if he is offended by a sloppy writing style. A dull style can make even the most exciting topic dull.
Good style is not easily achieved, and exceptional style is arguably due to genius, rather than adherence to any one set of rules and formulae. It is usually futile to take a great sentence from the work of a Conrad, Paine, or Tolstoy and explain why the sentence appeals to us in terms of rules and writing theory. However, we can usually explain in terms of broken rules why a poor sentence does not appeal to us. Thus it is our humble goal to eliminate poor sentences from our writing - and our earnest dream to write one or two great ones.