Rage allows your dragons to cast spells. Rage automatically regenerates with time.
When you are in battle, you can see a Rage meter on the left side of the screen that gradually fills up with time. When you cast a spell, it consumes some of your Rage. Stronger spells cost more Rage (e.g. the Summon Minion dragon spell costs 3 bars of Rage). Rage is shared by all dragons in an attack and transfers across rounds of attack.
TIP - Use your Hunter and Warrior dragons to earn Rage in the first round of Attack and then use you Sorcerer dragons to cast powerful spells in later rounds.