When you redesign a site, chances are that your structure may change and your URLs may change. If you don't plan ahead, you could throw away a lot of the search engine optimization you may have already achieved. When a search engine comes back to index your site again after a redesign, it will find that many (or all) of the old URLs no longer function and it will drop them and then reindex your new pages as new pages instead of as new versions of existing pages (which already have some ranking). Also, other sites may be linking to your site using old URLs (remember tip number three about external links?) and it would be a shame to throw that away. Of course, all this is not to mention the frustration your users may experience if they've bookmarked an old link or travel in to a 404 error page from a search result.
You can set up redirects manually using your .htaccess file or using a component or module for your shiny new content management system (which would give you an administrative interface to manage these redirects -- for example, the "Path Redirect" module for Drupal).
There have been a number of high-profile cases recently where this has not happened (notably the White House site, which dumped the previous site with a lot of its URLs "down the memory hole" and the New York Times, which erased a lot of content, many URLs, and one journalist's career when it wrapped the IHT site into its own).
With a little foresight and planning ahead, you can make the transition to your new site smoother for your users and retain as much search rank from your old site as possible.