Energy is used to progress in the Main Quest and Eternal Dungeon. It regenerates at a rate of 1 per 30 seconds up to the player's maximum determined by her level(?) and a guild bonus.
There are also yellow energy potions, which can be used to refill a players energy (50% or 100% depending on the potion's strength). Also, the elixir fully regenerates energy (together with health and stamina).