Archbishop is an ecclesiastical rank in Christianity above that of bishop and (in Catholicism) below that of Pope. Probably applies throughout SCA period, but was abandoned by the later Protestant churches, on the basis that each congregation ought to be autonomous under Christ.
It is not a rank one can award oneself. It really requires a number of bishops to support it.
In Modern Real Life, it is occasionally used as a means of establishing authority over a self-created sect.