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 you skin including the Vector extension, you can get similar functionality by editing your LocalSettings.php and adding