What do Wait and AP Bonuses do?

during an attack there are 3 bonuses

• SP Bonuses which comes from switching the type of attack

• AP Bonuses which comes from filling the gauge around the AP counter while using the same type of attack

• Wait Bonuses which comes from timing your next attack

I know that every SP Bonus you get SP but i don't get what Wait and AP Bonuses so what happens when you get these bonuses?

According to the mechanics description:

The Three Types of Battle Bonuses

When attacking with skills, taking special actions will get you various bonuses like AP and SP, as well as Wait reductions.

Motion Bonus

During an attack, you can earn an SP bonus by changing your target's motion state.

Limit Bonus

When you reach the absolute apogee of a particular motion while continuing to assault an enemy with certain motion attack moves, you can increase the amount of recovered AP. For example, when using the ∆ button to unleash a series of Burst attacks and launch them up into the air, you will receive an AP bonus if you hit the maximum elevation capable by that particular attack.

Strike Bonus

By successfully following up with another attack move at a specific time where the previous attack move is about to complete, Wait will decrease. When going for this bonus, time your button presses carefully; mashing will only hurt your cause.

They give you exactly what they say. AP bonus gives you more Action points than if you didn't get the bonus. Wait bonus gives a wait reduction. It's fairly straightforward.

Perhaps the wait mechanic is confusion you so here's some more information on it from the same page:

"Wait" and determining Action Order

Every skill has a Wait value attached to it that will increase every time the skill is used. The Wait value will determine when a character's turn will come around again once their current turn ends. The character with the lowest Wait value will have their turn come before any of the others.

This means that if a character's Wait value is low enough, they can sometimes perform consecutive actions. By paying attention to each of your party member's Wait value, it would be possible to take out an enemy with giving them the chance to retaliate.

You can reduce a character's Wait value by increasing their AGI or through equipment bonuses.

Having less wait allows you to take action sooner so you won't have to sit as long with AP in order to reduce wait. It also acts to avoid the Overwait status because you will accrue less wait.

I'm not sure how to better explain Action Points (AP) than the game does on it's own. They are points you spend for certain actions. The bonus increases the amount recovered.

The bonuses aren't huge, but can be game changing in tough situations.