These options allow you to control how the XML sitemap is generated and submitted to search engines. The sitemap can be used to speed up search engine indexing of your site.
Automatically build sitemap
If this option is enabled, the sitemap will be rebuilt automatically periodically. If this option is disabled, the sitemap will only be updated when it is rebuilt manually through Tools > Rebuild Caches. The current sitemap can be accessed via sitemap.php.
Automatically submit sitemap to search engines
Once a sitemap is built, if this option is enabled, the updated version will be automatically submitted to search engines. If this option is not enabled, search engines will only know about the sitemap if it is listed in robots.txt or if you manually submit it to them.
Telling search engines where it is is useful and doesn't take much time. For example you can add it to the Google Webmasters or Bing Webmaster Tools, and they are relatively quick to start using it. You'd also get feedback, like which urls are in the sitemap but not accessible and which pages have been indexed.