The Sovereign is the Supreme Governor of the Church of England. The Head of the Church is Christ, not the Sovereign.
Although the Act of Supremacy of 1534 gave Henry VIII the style "supreme head of the Church of England", doubts were expressed about it and when the Act was reaffirmed by a similar Act in 1559 (having been repealed by Queen Mary I in 1555) the title "supreme governor" was used.
The sovereign appoints bishops who are elected by their electors1 and the Crown has rights in certain Church of England parishes. The Crown governs the Church of England through primary legislation passed either by Parliament or the Church's General Synod.
The Archbishop of Canterbury is Primate of All England (a title conferred by Pope Innocent VI and confirmed by the House of Lords Precedence Act 1539). He is the senior bishop in the Church of England and by convention the "first among equals" within the Anglican Communion.
1 This isn't quite as democratic as it seems: the Crown has a big part to play in presenting the single candidate for the electors to vote on.