A Might Score is a measure of your character's power! It tells you just how strong you or your opponents are.
Might Score is calculated by adding your character's base Might - which is related to a character's level - and adding up the Might of each piece of Equipment in use, as well as the Runes inset into their gear. Also taken into account are the Might levels of all the Pets currently set to join the hero in battle.
The Might Score can be found in the top left corner, near the name and character info.