Health refers to how much damage you can take before you die. Your Health Bar shows how much health you have at any time. When your Health Bar is empty, you die. When you die, you will drop all of your items (unless keep inventory is on) and respawn at the last bed you slept at (or at the default spawn if you have not slept).
If take damage, your health will decrease based on the attack. If your hunger bar gets completely depleted you will not die, but you will not be able to replenish your health - thus making you an easy kill for enemies. If your Food Bar has 9 or more of the pictures shown,yet your health is low,it automatically replenishes your health.