At each level characters receive 1d3 Action Points. An action point can be used to re-roll any failed roll once, or otherwise influence events to the benefit of the party, at the discretion of the Dungeon Master. Typically these are situations where the player is rolling a d20, or the GM is rolling a d20 on behalf of the player. Action Points cannot be converted to Character Points.
Spending the Action Point to reroll makes it as if he first roll had never happened (the player does not get to pick between the better of the two rolls). You cannot use multiple action points on the same roll.