Hit Points are how much damage you can take before you collapse and wake up in the clinic.
When you lose all your hit points there is a good chance you'll wake up with a cold the next day. You will also start the day with half HP and/or half RP. If an enemy monsters hit points are reduced to 0, it will fade to the first forest and will be re-spawned by its gate once all monsters of the gate are in the first forest. If a pet monsters hit points are reduced to 0, it will teleport to the barn and lose some friendship with you, so it is recommended to send it to the barn by talking to it just prior to its defeat.
To prevent this, one can use almost all food and medicine for regeneration, most effectively the energy drinks.
Hit points can be lost by being hit by an enemy attack, in which case the enemy's attack is subtracted by your defence to determine damage, or by being poisoned, which will cause you to lose one tenth of your hit point total every few seconds, but will not kill you but rather stop damaging at 1 hit point.