The emperor is the Emperor of all of Tamriel. Then below the emperor would be the king of each province (High King of Skyrim for example), below the king would be the Jarls, dukes, stuff of that sort.
Its a class system basically, used for better management/ control of lands etc.
It's a feudal system, yes. The Empire doesn't encompass all of Tamriel any more, though. Basically, the Empire as the game takes place is only made up by Cyrodiil, High Rock and Skyrim. The Thalmor control Summerset Isles -- now renamed Alinor -- and Valenvood. They have allies in Elsweyr.
Black Marsh -- now renamed Argonia? -- has invaded Morrowind. Hammerfell has broken off with the Empire and the war between Hammerfell and the Aldmeri Dominion has ended in the second truce at Stros M'Kai.