Activity Points is a sub-category stat and a third-bar used on various classes, the purpose of this stat vary and the way to acquire and use it also change with the classes. Some is to increase damage or to generate bonuses, others may use as a Requisite to cast a skill, and so on.
Some classes may have AP but they wont use it at all, you can check on this page all classes that actually use it.
Activity Points are show on your character information with AP 0/X meaning X is the maximum you can store, different classes have different amount of AP. You can also see your points bellow your SP/HP bars, with a Yellow Color.
Classes
Monks
Monk Combo
For Monks your Activity Points will be used as Combo Points, and a maximum of 5 can be stored.
While fighting you can see your bar filing up, you can store all the 5 using the monk skills and expend it all at once on a skill that consumes it like Tiger Fist and Throw Spirit Sphere
Each Combo Point will buff those skill damage by a % of damage See skills.
Combo Points can be used anytime, you dont need to wait it fill up at 5.
Combo Points have no Cooldown of any kind, you can acquire points everytime you use skills, meaning the speed you cast those skills is the same you acquire Points.