A character uses his move action to move through a threatened space. He wants to avoid AoO, so he uses the Acrobatics skill to avoid provoking one. Assuming the skill check succeeds, the opponent never has the chance to make an AoO, therefore his AoO is not used for the round and he is free to decide whether to make one or not the next time one is provoked.
For completeness, from the pathfinder FAQ:
Acrobatics allows you to make checks to move through the threatened area of foes without provoking attacks of opportunity. You must make a check the moment you attempt to leave a square threatened by an enemy, but only once per foe. The DC (which is based of the Combat Maneuver Defense of each foe), increases by +2 for each foe after the first in one round. The DC also increases by +5 if you attempt to move through a foe. In the case of moving out of the threatened square of two foes at the same time, the moving character decides which check to make first.
For example, a rogue is flanked by a meek goblin and a terrifying antipaladin. The rogue move away from both of them, provoking an attack of opportunity from both, but uses Acrobatics to attempt to negate them. She must move at half speed while threatened by these foes and can choose which to check against first. If she fails a check, she provokes an attack of opportunity from that foe. If she makes it, she does not provoke from moving through that foe's threatened space this turn.
Also note that negating AoO in this way is completely independent from if that creature makes the attack. You could attempt to avoid provoking an AoO on a creature that can't make any more this round, and a creature can choose not to attack even if you do provoke one.