Bleeding is a damage over time effect, represented by a red drop. At the beginning of your turn you will take damage. Lasts for a certain amount of turns.
By hovering over the red drop you can see how much damage your hero will take. (Example: 2 damge for 3 rounds)
Bleeding can be removed earlier by right-clicking on the provision bandages. If not cured the effect will continue even after the battle is won.