Action Points were one of the individual character stats from the original release of Final Fantasy XIV, each discipline having its own amount based on its current level.
Each ability (with the exception of some 'normal' attack variants and the MP recovery ability used by the Disciples of Magic) had a certain cost in Action Points that had to be used for it to be set, be it on the Action Bar or as a Trait, effectively limiting how many skills a character could have equipped at the same time. Abilities could not be changed during a battle, and there was no extra Action Point cost for using cross-discipline abilities.
The Action Point cost for skills was removed in patch 1.20 of Legacy. After that patch, players were able to use all skills from their own class at all times, and could set a number of other classes' skills based on their current class level, with a maximum of 10 at level 50. This system was retained in full for A Realm Reborn. However, the term "Action Points" would later be reused in a different context for the player-versus-player modes as a mechanic for upgrading PvP exclusive abilities and traits.