Health is a measure of how much damage you can take before dying. It's shown over top of a heart on the main page, and as a bar at the bottom while dashing.
Dash starts with 20 health and gains 5 per level (10 at level 6?) up to max level. All Armor and some accessories add to maximum health as well. Legend bonuses and perks can increase max health.
Different potions and items can restore health, and bosses and rare monsters drop some automatic healing. The Fairy pet will also heal. The spells Recover and Heal can also be used to restore health.