Manual:$wgAjaxSearch

Details
When true, this enables auto-suggestion for the search bar, using asynchronous javascript XML requests.

This also requires $wgUseAjax to be true.

Setting $wgAjaxSearch = true; causes wfSajaxSearch to be added to $wgAjaxExportList

mediawiki/skins/common/ajaxsearch.js is used to deliver the content. The script defines where on the page, and when the ajax search results will be delivered.