Health is a representation of your current life value. If your health reaches 0, you are dead. When your health is at or below 30 HP, your character becomes Injured, and will move much slower. You will have to regenerate your health by eating Cooked Meat, using consumables like Blood Pack or Medical Brew, or through natural regeneration in order to regain normal functionality. Being attacked, falling, drowning, and extreme Temperatures can all lower your health.
Putting a skill point into Health will increase your maximum health by 10.
Adding points to health only increases maximum health. It does not increase current health. This means you cannot gain extra health immediately in the combat and you have to do it before that, and wait and let your or your tames' health to regenerate to become effective.
After 50% of health has been lost, you will begin to hear the sound of your own heartbeat and heavy breathing. The lower your health gets the louder the sound will get.
Wearing armor will decrease the amount of health lost from most damage sources, and therefore increase your effective health. This "effective" health is not counted towards certain situations, such as suffocation or falling.
Increasing health will actually slightly help you with food, water, and oxygen, simply by the fact that you can starve or suffocate for longer before becoming injured or dying.