With a page parameter, specify a particular parent page to display the template for. Potentially useful for subpages of subtropes, but mainly done for parallelism with {{work}}. This is what {{trope|page=Lampshade Hanging}} produces:
With a wppage parameter, specify a particular Wikipedia article to link to. This is useful for when Wikipedia has an article on the subject in question, but its title doesn't match up. This is what {{trope|wppage=Chintzware}} produces: