Every dragon has an element. Each element is stronger or weaker to another element. The Shadow Element is an exception as it's neither stronger nor weaker to any other elements. Exploring Hero Mode with a dragon of corresponding element to the area will grant it a 10% buff on its ATK, DEF and HP (e.g. exploring Forest of Hope with a Boulder Dragon).
The O means the attacking element is strong against the defending element and the X means the attacking element is weak on the defending element.