Stamina represents your character's physical endurance. If your character is injured, the character's stamina decreases. There are Items, Spells, Events, and other ways to restore stamina as well, though Stamina cannot exceed the character's maximum.
Having Stamina drop to 9 or below will change the player character's appearance on their portrait, making them appear visibly injured.
If your character's stamina drops to zero or lower, they die. However, if the combat mode is set to "Last Stand", then, if a character's stamina drops to zero or lower during battle, the character will only die when starting a new encounter or dropping below -5 stamina. While a character's stamina (or reason) is zero or lower, the face portrait is covered with black stains, presumably blood.