Critical hit

Critical hits are attacks that deal extra damage compared to regular attacks. Critical melee strikes, regardless of the weapon used, cause small star particles to fly out of the target who was critically hit. "Critical arrows", which occur when the bow is fired fully charged, leave a trail of the same small star particles as they fly through the air.

Critical hits affect all damageable entities including Players, Mobs, Paintings, Boats and Minecarts.

Critical Hits in Melee
In melee, a critical hit occurs when a player attacks a mob while falling. The attack deals 50% more (rounded down) plus one heart of damage. This can be done by jumping. It can also be combined with sprinting to knock back the mob, although there is no extra knockback for a critical hit.

In an Abandoned Mine Shaft, a player may choose to jump into a cobweb. At the cost of mobility, the player will be granted a major damage increase, as cobwebs greatly extend the time the player falls. This same tactic can also be used when descending in water.

Critical Damage
This is a chart cross-referencing weapons with materials to find the amount of damage dealt from critical hits while falling in version 1.8.

As fists do not have a "material", their damage is constant. Although Hoes are tools, they are not counted as weapons and have the same effect as fists (no durability loss and same damage)

Trivia

 * Critical hits can be done while reflecting a Ghast's fireball, but won't change the damage or speed of it.
 * In Creative mode, attacking a mob while flying, after floating down, will get a critical hit.

Fighting Tutorial
Basic Fighting Mechanics

Kritischer Treffer Критический удар