Your Hitpoints (HP) are shown in the red bar on the top left of the battle screen. They show how much damage you can be dealt before dying.The maximum can be inceasted by potions/other consumables/Getting the wanted item in a dungeon or by equipped items. You lose 1 maximum Hit Point after death.
Health Points are also used in Defense Quests and the quest "Nasty Necros" (Tier 3 - Challenging) gives a "Potion of Health" and when drunk, adds 3 Max Hit Points. It's a slow but easy (if you have high enough skill) way to get Max HP.