A good understanding of the game and a tactical sense
A coach is responsible for the level of play of his or her team, and in order to properly communicate football tactics and techniques, he or she must master them himself or herself. Certain players will find it difficult to respect a trainer who doesn't try to set up a certain system of play or who has a hard time grasping the differences between tactical formations.
This type of deep understanding will allow you to make good decisions at match time. Making adjustments to your team based on your opponent, or making the right substitution at the right time, can totally change the direction of a match. Would France have won the Euro 2000 without Pirès, Wiltord and Trezeguet coming on as subs? Quite possibly not.