Use this setting to configure the dropdown mode for search boxes in this site collection. The dropdown can include Contextual ...

Use this setting to configure the dropdown mode for search boxes in this site collection.  The dropdown can include Contextual or Custom Scopes.  The dropdown can show in the interface, or it can not show and simply direct searches to a default scope.

By default, a Search Box will use the "Dropdown Mode" property in the web part. By checking the "Use site dropdown mode" property, the search box will use this "Site Collection Search Dropdown Mode" setting instead.