Manual:$wgEnableMWSuggest

Details
Enable AJAX autocomplete search suggestions (autosuggest) while typing in search boxes (results are passed around in OpenSearch format).

This setting replaces $wgAjaxSearch that was used in earlier versions of MW.

If you want to turn off autosuggestions now (as the feature has been removed), use $wgEnableOpenSearchSuggest.

Alternatives
If you are using any version above 1.19 and also using Vector as your skin, you can get similar functionality by editing your LocalSettings.php and adding $wgVectorUseSimpleSearch = true;