CSS is inspired by the style sheets of yore, of typeset publications made by ink-smeared metal pressed into paper. A magazine or newspaper might have a "style sheet" that said things like, "Paragraphs shall be 10-point Caslon" and "all second-level headings shall be hanging headings, outdented 5 picas." Before web browsers got a hold of them, stylesheets had already entered the electronic world in desktop-publishing software like QuarkXPress and even Microsoft Word.
The problem they were trying to solve was, how do you update the look and feel your website easily? This was in the days when most websites were static HTML files, and updating all your articles meant changing a file for every page. The most famous and beautiful example of the power of Cascading Style Sheets is CSS Zen Garden. In 2003 Dave Shea provided an unstyled page of HTML, and then designers from around the world contributed stylesheets that transformed the page into wildly different designs (http://www.csszengarden.com/).