LaTeX aims to be a general-purpose document processor. Such an aim
could be achieved by a selection of instructions which would enable
users to use TeX primitives, but such a procedure is considered too
inflexible (and probably too daunting for ordinary users). Thus the
designers of LaTeX created a model which offered an
abstraction of the design of documents. Obviously, not all
documents can look the same (even with the defocussed eye of
abstraction), so the model uses classes of document. Base
LaTeX offers five classes of document: book,
report, article and letter.
For each class, LaTeX provides a class file; the user
arranges to use it via a
\documentclass command at the top of the
document. So a document starting
may be called “an article document”.
This is a good scheme, but it has a glaring flaw: the actual typographical designs provided by the LaTeX class files aren’t widely liked. The way around this is to refine the class. To refine a class, a programmer may write a new class file that loads an existing class, and then does its own thing with the document design.
If the user finds such a refined class, all is well, but if not, the common way is to load a package (or several).
The LaTeX distribution, itself, provides rather few package files, but there are lots of them, by a wide variety of authors, to be found on the archives. Several packages are designed just to adjust the design of a document — using such packages achieves what the programmer might have achieved by refining the class.
Other packages provide new facilities: for example, the graphics package (actually provided as part of any LaTeX distribution) allows the user to load externally-provided graphics into a document, and the hyperref package enables the user to construct hyper-references within a document.
On disc, class and package files only appear different by virtue of their name “extension” — class files are called *.cls while package files are called *.sty. Thus we find that the LaTeX standard article class is represented on disc by a file called article.cls, while the hyperref package is represented on disc by a file called hyperref.sty.
The class vs. package distinction was not clear in LaTeX 2.09 — everything was called a style (“document style” or “document style option”). It doesn’t really matter that the nomenclature has changed: the important requirement is to understand what other people are talking about.
This answer last edited: 2013-10-21