With an overdrove - AP weapon equiped anything that raises a character's overdrive gauge will no longer do so - instead the guage will stay still and the amount of overdrive you were supposed to get is converted into AP. So lets say that the overdrive mode for yuna was 'stoic' this means that her overdrive guage fills when she is hit by an enemy. The higher the enemy's attack - the more her overdrive guage fills. There is also a relation between the amount of overdrive you get with the amount of hp your character has. If Yuna had like - 2000 hp and was dealt 80,00 damage from Don Tonberry it would raise the overdrive gauge more (the amount of AP in this case) than a Yuna with 20,000 hp because the is a smaller difference in ratio between the stats.

That's why it is best for a charcter to have low hp - be in stoic overdrive mode and have killed a lot of enemies because then DT wil deal a hell load of damage and give you tonnes of overdrive which is converted to AP.

For even more AP you can further customise a weapon with the abilities - triple overdrive and triple AP. This literally triples the overdrive you receive from DT damage therefore giving you triple the AP. AND THEN... the triple AP will times this AP by three again - you will literally get 99 sphere level in one fight!!!!!