energy is for training pets and gardening. You use the energy to play pet mini-games to train pets. You also use it for planting and caring for a garden.
When ever you play a pet game to train your pet you use energy. If you have no energy, the game won't let you play pet training games. When you cast a gardening spell you use energy instead of mana. Pet spells can be purchased at the mole in golem court. If you have no energy you can't garden. Energy refills at one point per minute.