High Stamina is important in battle, because Energy is used for moving, throwing, melee and magical attacks - eventually you will lose your breath.
Sprinting (CTRL+move) will allow you to run faster, but will burn through any amount of Energy rather quickly.
You can alleviate the problem a bit by dressing as lightly as possible, but real endurance can be achieved only through training.
The Energy recovered per turn is normally equal to one fifth of current Freshness % + one quarter of the current Health.