A critical strike is a basic attack that deals twice its normal damage. In the real world, it's an attack striking a vulnerable area, while in other MMO and/or RPG settings, it ties into the very common "critical hit" mechanic.
It only applies to basic attacks or certain abilities like Hei's Hei [Q] and Kuroba Kaito's Magic Prop [Q] that act like a basic attack or Tachibana Kanade's Hand Sonic [Q] and Dracule Mihawk's Kokutou Issen [Q], which are specially stated. It's important to note that you cannot score a critical strike against a building such as a turret or an inhibitor.
Most heroes have different attack animations for a critical strike, though some do not; this includes mages and other heroes not meant to be built using basic attacks for damage. Some of these heroes performing a critical strike (if built being able to perform them) may instead have a soundbite that plays in place of an animation, typically a grunt of effort.
Critical strike is valuable for all heroes who primarily deal damage with basic attacks, rather than through abilities. Some heroes, such as Kirikage Archer, have an affinity for critical hits and benefit more from items that improve them. Players can increase the Chance and the Damage of critical strikes with items and abilities.
Critical strike chance or critical rate, as the name states, is the chance of a hero's physical attacks dealing a critical strike. Critical strike chance stacks additively. Items and some abilities can increase critical strike chance.
The maximum critical strike chance you can reach is hard capped at 100%.
Critical strike damage refers to the amount of damage that a heroes critical strike will deal. All heroes have 200% critical strike damage by default. In most cases, critical strike damage stacks additively. Damage modifiers apply to critical strike damage normally.