Web Design relates to the creation of your sites "visual look and feel."  The user interface and navigation of the site.  Your site's color scheme and how it looks with your company or site logo.  Design is an important aspect to your online presence.  Without it, people will not take your company seriously.

Web Development describes the process of making your site work.  It is the fundamental programming that determines what features are available and how they work.  Good programming work is typically overlooked by most users, but without good development, you could have the prettiest site in the world, but there would be nothing to do -- no functionality.