Dragon Points are used for discovering and upgrading Dragon Arts. Fighting and slaying Monsters in the Battle tab of the Dragon Stone will earn you Dragon Points, after which you can check how many Points you have earned by visiting the Dragon tab.
In order to earn more Dragon Points for fighting Monsters, you need to discover and upgrade the "Master of Monsters" Dragon Art. Please note: If you select this Dragon Art and activate its Bonus while still fighting a Monster, the Bonus will not become active until after that Monster has been slayed. However, the bonus will be applied to the next Monster you defeat.
Dragon Marks are required for activation of Arcane Dragon Arts, as well as for discovering the Dragon Art "3rd Additional Slot". Dragon Marks can only be earned during Tournaments.