If you click the enemy to make an auto attack, then use q and target the enemy, annie walks into range and throws her q, then, when q animation is over, she throws another auto attack.
If you walk into range of annie's q, click to auto attack, you can IMMEDIATELY cast q, canceling the auto attack animation (after the fireball comes out) No sooner does Annie perfor the animation for her q, you immediately click the enemy to manually input an attack command. Annie will immediately perform an auto attack without waiting for the frames of her q to stop.
Consider Viktor's q. It empowers his next basic attack. If you just q a minion, he'll use q, perform animation, then use his empowered auto. But if someone were to click to q a minion and immediately after input the attack command, before the q even comes back to Viktor he nearly instatly performs the empowered auto.
Very small time window, but it makes big differences often.
Auto attackQAuto attack = Use this often and get used to it it's your bread and butter combo and it's how alot of champs chain their moves.