Question

What are the duties of an archbishop

Answer 1

Basically supervise all other bishops

Answer 2

The bishop of the more important cities, or of historically important places, is given the title of Archbishop, to show a level of seniority or honour.
 From the original Greek word for ‘overseer’ (episkopos) we get the English word ‘bishop’. Ever since the beginning of the second century, every portion of the Catholic Church, or local area called a ‘diocese’, has been headed by a bishop, who has the duty to teach, sanctify (meaning, make holy) and govern God’s people.