Once enabled, Search Boxes will show custom scopes to the user in the scopes dropdown. Custom scopes can be defined in either ...

Once enabled, Search Boxes will show custom scopes to the user in the scopes dropdown.  Custom scopes can be defined in either this Site Collection or the Search Service scopes pages.  Queries will be sent to the Search Center URL with the scope's results page appended.

By checking the "Use site level defaults" web part property, the search box will send custom scope queries to the Search Center defined in this "Site Collection Search Center" property.