Since K2 v2.5.0, we are not using the Mootools javascript library that's bundled with Joomla!, but instead use the more flexible jQuery javascript library. This allows us to write code once and still be able to support both "major" versions of Joomla! (1.5 and 1.6/1.7).
When you set the jQuery library handling option to "remote 1.6", it means you use Google's servers (CDN) to fetch this JS library, which basically makes your site load faster (as your browser sees more "download" channels to get content from).