I ask because over at Commentary that distinguished man of theatre, Mr. Terry Teachout, asks the same question. He reminds us that the whole notion of a director is relatively recent. In Shakespeare's day at the original Globe Theatre, the role simply did not exist although I would venture to suggest that some sort of directing hand (or hands) must have operated simply to ensure that actors entered and exited at the correct places carrying, where necessary, the correct artefacts. In the late 19th century, the age of the actor/director arrived in which the most famous actors, and therefor the leaders of their companies, would literally order where and when the actors would move and how they would deliver their lines. It was in the 20th century that the modern notion of the director would come into being and would rapidly ascend to a position of ultimate power.
So what do they actually do? In my opinion, they should do everything! Well, everything except act, that is. Obviously, the very first thing they need to do is study the play - in depth! - in detail! - from every direction! - in an attempt to discern what the playwright was attempting to say. That is not easy to do when the poor, old scribbler has been dead for a few hundred years but it must be attempted because, and this is frequently ignored or forgotten, the director is there to serve the writer! From that point on, the director must attend to every facet of the production - set design and furnishings, lighting, sound, costumes, make-up, special effects, entrances and exits, movements on stage, music and so on and on.
In other words, a director needs what our American 'cousins' would call 'that vision thang!' Needless to say, directors might with great honour and seriousness attempt to serve the writer and then miss by a mile - and yes, you're right, I know where-of I write. If that happens, of course, there is only one way to deal with it, you simply blame the actors!