Green XP points are needed in order to level up your Event Level in Story Events. While you would normally merge and collect Blue XP points in order to increase your level in the game, green XP points do the same but in Story Events; they let you level up by collecting them.

The amount of green XP points you need to level up varies on the Story Event you are playing, as well as on what level you are. For example, if you are playing the Ignatius Boulton Event, you start off with Event Level 0 and in order to reach Event Level 1, you need to collect 41 green XP points. To go to Level 2, there would be an increasing amount of required Green XP points.