Action points (AP) are the resource used by characters to perform actions - skills, spells, etc. Action points recharge gradually over time, with a higher rate of recharge when your character is not involved in combat. All characters currently have a maximum value of 250 AP.
To compare it with another game's similar mechanics, World of Warcraft's (WoW) rogue has something called energy that has a "absolute" value 100 (can get more from items/talents). Unlike WoW, all characters in WAR use Action Points.
Currently, the costs for actions range from 8 to 130 Action Points, depending on many factors like the effect of an attack.
The use of Action Points leads to very little down time because you are constantly regenerating it. Where other games require you to use potions, food, and/or drinks to regenerate (or at least accelerate to a reasonable rate the regeneration of) your energy, or whatever you call it. You can still use potions to achieve similar effects in WAR, it is just not required.
Characters regenerate 25 AP per second in game when not in global cooldown from using an ability. Items that give +AP regeneration increase this value. So +5 AP regen is a 20% boost to action point regeneration.