I'm not an instructor, but I'm going with developing a) good stroke fundamentals, b) sound angle management practices, and c) refined speed control.
SJM might be the best instructor that denies being one! Some of the things he says here incorporate other things you must have for these to work but this is as good of grouping of three things as I have seen. While he didn't mention reading patterns, it is impossible to play speed and angles properly without first knowing what you are trying to do so his list incorporates pattern play without listing it.
If I listed three things it would be reading patterns and cue ball control. One choice left over. Like SJM's listing, mine incorporates other things. If you have cue ball control you will pocket the object balls, just a given. I lump cue ball speed and angles into one listing, they are as readily broken out as Stu did.
Like Willie Mosconi's claim of pool being a very simple game, the theory I believe in is very simple. See where the cue ball needs to go, put it there. That requires reading the entire pattern. At first backwards from the money ball then frontwards, after enough table reading it can just be read frontwards. With the entire inning planned and cue ball control, difficulties have been planned through before ever getting to them. While it can happen when taking over from another player or after the break, during a run try to avoid having both sides of a shot being difficult. If pocketing the ball is hard, I want it to be easy to play shape. Likewise, if shape is going to be a little tricky, I want pocketing the ball to be easy. Most runs can be planned to work out this way, at least one side of the shot easy.
I guess I'll use up that last thing to list before leaving. Minimal cue ball movement. The less the cue ball moves the less chance it has of getting in trouble!
Hu