(I have yet to find a captioned Al Jazeera film, which makes them inaccessible, like this one.)

A Caliph is a leader of the Muslim community - a combination of religious and political/military leader, with greater emphasis on one or the other aspect depending on the leader. Their understood mandate is to expand the Muslim community through conquest or other means. 

From this, a Caliphate is the period and area ruled by a particular Caliph.