Hero Points (also known as Stars) affect your characters stats. No stars means that your hero is fighting without a bonus. They will fight better the more stars they have up to five the maximum. Stars make your character slightly stronger than usual and allows you to survive especially difficult encounters.
A character gains Stars by completing missions and defeating villains. A character loses one star each time they are defeated.
The Stars are displayed along the bottom edge of the player portrait, in the upper-left corner of the UI (by default).
There are vendors in each map usually posing as some sort of relief or charity worker where you can donate resources to replenish one or all of your Hero Points.
A character with all 5 stars has a plus 15% damage and healing bonus added. A character with zero stars is fighting as normal. There is no death penalty in the game other than losing your bonus.