When my family and I discuss what makes a good quarterback I think about what actually is a GOOD quarterback? When you see it, what exactly is it that you are seeing? I think a good quarterback at the end of the day helps their team get the win.
Weekly Preparation
During the week the coaches will draw up a game plan, generally enough plays for the first one or two drives of the game. This game plan is based on the coach studying film of the opponent and deciding at least two things 1: How to exploit the other teams weakness 2: What does the team do well that he feels the opponent just will not be able to stop. Depending on how good the quarterback is, the quarterback will have some input into this game plan.
Average Quarterback
An average quarterback will be able to execute the coaches game plan. The quarterback will avoid a sack or two and throw the ball away if the first read is not there. If the team scores, great. If the team does not score, a good quarterback will at least not turn the ball over and not be the reason the team loses.
Good Quarterback
A good quarterback will do everything an average quarterback does and more. The quarterback will go through all of their reads and avoid most sacks. A good quarterback will take what the defense gives them. The quarterback will implement the coaches in-game adjustments based on what worked in the gameplan and what the opponent is doing. A good quarterback will make a play or two happen using their unique talent (running ability, strong arm, etc.). A good quarterback is separated from an average quarterback usually by talent and utilizing the full game plan and all of their teammates (not just the main target).
Great Quarterback
A great quarterback will do everything a good quarterback does and more. The quarterback will read the defense pre-snap and make effective changes to the play call. A great quarterback will suggest in-game adjustments based on what they are seeing. A great quarterback knows how defenses work and can throw a receiver open. The quarterback understands situational football and timeouts, always making sure the team is in the best situation to win. A great quarterback does not rely on a unique talent (running ability, strong arm, etc.) to win games (i.e. play hero ball).
I think the most important item that makes a quarterback great is that they make their teammates better. A great quarterback does not need a great receiver, great running back, great tight end, great o-line, great defense, and a great coaching staff. One or two (or sometimes none) of those things will do. A great quarterback loves the game of football. His teammates can feel that. His dedication is automatic, he wants to be in the film room. He wants the ball in his hands at the end of the game. He wants to run the first couple of plays, see what the defense does, then go back on the next drive and pick them apart. A great quarterback understands the weapons around him and caters his throws to their strengths. They will throw the ball away, check down, run if no one is there and there is space in front of them. A great quarterback seemingly always makes a positive play. A great quarterback wins in the playoffs.