Topic on Extension talk:Semantic Page Series

Where is this parser function used, in the same place (the template for the page referenced by the form) as #set_internal_recurring_event?

You could put it there, although it has a very different function than #set_internal_recurring_event. Where #set_internal_recurring_event specifies the recurring events, the #serieslink will take you to a form, where you can put in some data. The #serieslink is more similar in function to #formlink, so wherever you would put a #formlink, you could put a #serieslink.