Why does URL mapping and rewriting matter?
The most common scenarios where developers want greater flexibility with URLs are:
1) Handling cases where you want to restructure the pages within your web application, and you want to ensure that people who have bookmarked old URLs don't break when you move pages around. Url-rewriting enables you to transparently forward requests to the new page location without breaking browsers.
2) Improving the search relevancy of pages on your site with search engines like Google, Yahoo and Live. Specifically, URL Rewriting can often make it easier to embed common keywords into the URLs of the pages on your sites, which can often increase the chance of someone clicking your link. Moving from using querystring arguments to instead use fully qualified URL's can also in some cases increase your priority in search engine results. Using techniques that force referring links to use the same case and URL entrypoint (for example: weblogs.asp.net/scottgu instead of weblogs.asp.net/scottgu/default.aspx) can also avoid diluting your pagerank across multiple URLs, and increase your search results.
In a world where search engines increasingly drive traffic to sites, extracting any little improvement in your page ranking can yield very good ROI to your business. Increasingly this is driving developers to use URL-Rewriting and other SEO (search engine optimization) techniques to optimize sites (note that SEO is a fast moving space, and the recommendations for increasing your search relevancy evolve monthly). For a list of some good search engine optimization suggestions, I'd recommend reading the SSW Rules to Better Google Rankings, as well as MarketPosition's article on how URLs can affect top search engine ranking.