Hit Points

Hit points are a measure of how much exertion, pain, or harm a creature or object can take. Nothing can ever have more hit points than its hit point maximum; similarly, nothing can ever have fewer than 0 hit points. If an effect would change a target's hit points past either of these bounds, it changes the target's hit points to the limiting bound instead.
As a player, your hit point maximum is determined by your class. Other effects may temporarily or permanently modify a creature's hit point maximum, including yours.
A creature is bloodied if it has less than or equal to half its maximum number of hit point. This is the point at which the creature's body shows obvious signs of harm. In general, it is possible to tell at a glance whether a creature is bloodied.

Damage

Whenever a creature or object takes damage, it loses a number of hit points equal to the damage taken. As stated above, if damage would reduce a target's number of hit points to below 0, its number of hit points is reduced to 0 instead.

Damage Type

Each instance of damage is associated with a damage type. There are 13 damage types in total, listed below. Damage types don't have inherent rules associated with them; they are merely labels that other rules refer to.
Damage Types
TypeCaused By
BludgeoningBlunt impact, such as by a hammer.
PiercingSharp points, such as on an arrow.
SlashingSharp edges, such as on a sword.
AcidAcid, and similar caustic substances and chemical reactions.
ColdLow temperatures.
FireHigh temperatures.
ForceSpatial warping and raw magical energy.
LightningElectrical currents.
NecroticDecay, either natural or supernatural.
PoisonPoison, and similar toxic substances and biological disruption.
PsychicMental and emotional trauma, including pain of all kinds.
RadiantIntense light, including non-visible light.
ThunderLoud noises and similar vibrations.

Damage Modifiers

Some creatures and objects take more or less damage from certain types:
When determining how much damage a target takes, apply immunity first, resistance and vulnerability second, and reduction third. If a target is both resistant and vulnerable to a damage type, the effects cancel, no matter how many distinct "sources" of resistance and vulnerability the target has (similar to advantage and disadvantage). Consider the following examples:

Dropping to 0 Hit Points

When a creature is reduced to 0 hit points, it falls unconscious, gains 1 level of exhaustion, and begins dying. Objects aren't so lucky; they are simply destroyed upon dropping to 0 hit points.

Variant Rule: Instant NPC Death

It can be burdensome for the DM to track the death saving throws of every dying creature. The DM may elect for most creatures to die instantly upon being reduced to 0 hit points. As a middle ground, the DM might only track death saving throws for creatures reduced exactly to zero hit points, without any excess damage.

Temporary Hit Points

Temporary hit points are special hit points that are tracked separately from your normal hit points. When you take damage, reduce your temporary hit points first (to a minimum of 0), and only reduce your normal hit points by excess damage.
Temporary hit points aren't cumulative. If you gain temporary hit points while you already have some, you must either lose your existing temporary hit points or forego the new temporary hit points.
Unless otherwise specified, temporary hit points disappear when you finish a long rest.