Stacking has two meanings, the one being used can be deduced from the context. Effect stacking occurs when a single effect is applied more than once to a target. Stats stacking occurs when stats are modified by multiple effects.
Effect stacking
Champion abilities, summoner spells, items, and buffs often apply effects to characters. Different effects always stack with each other. However, one the same effect is applied several times to the same unit, sometimes it stacks and sometimes it doesn't.
When a non-stacking effect is applied to a target that already has the effect the duration of the effect is reset to the duration of the most recent application.
When a stacking effect is applied to a target that already has the effect:
- The number of stacks of that effect increases by one, unless the maximum number of stacks has been reached. For example,
Jinx's 
Rev'd up stacks up to 3 times. - The duration of all stacks is reset to the duration of the most recent application.
Example: if Jinx has 1 stack of Rev'd up with 1 second left and gets another, the duration of the first stack resets to the full 2.5 seconds.
Some stacking effects are just counters building up to a different effect (e.g. 
Caitlyn's 
Headshot). Most effects, though, have their potency multiplied by the number of stacks.
- Example: if Ezreal has 5 stacks of
Rising Spell Force, his attack speed is increased by 50% rather than 10%..
Aura stacking
Aura effects don't stack with themselves: If champion A and champion B are generating the same aura, and champion C is affected by both auras, champion C receives the effect of these auras only once. However, for the purposes of stacking, the effect received by the champion who creates an aura is different than the effect received by a champion standing nearby. Since those effects are considered different, they do stack with each other. This has practical importance when two champions who generate the same aura are close to each other. Each of them receives the aura effect duplicated: They receive the aura effect from the aura they are creating, but also from the aura created by their ally. Since both effects are considered different, they stack with each other.
Champion statistic stacking
Some in-game values can be modified by multiple effects. It can be said that a champion statistic stacks additively or stacks multiplicatively.
Stacks additively
When effects stack additively, the cumulative effect can be calculated simply by adding together each effect.
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- Example: if your champion has two items granting +100 health each, your champion has 200 bonus health.
Effects that stack additively
- Ability power
- Armor
- Armor penetration, flat
- Armor reduction, flat
- Attack damage
- Attack speed (has a hard cap)
- Cooldown reduction (has a hard cap)
- Critical strike chance
- Critical strike damage
- Damage amplification
- Health
- Health regeneration
- Life steal
- Magic penetration, flat
- Magic resistance
- Magic resistance reduction, flat
- Mana
- Mana regeneration
- Slow resist
- Spell vamp
Stacks multiplicatively
When effects stack multiplicatively, the cumulative effect can be calculated by multiplying the effects together. Note that the game interface rounds champion statistics, so what is shown in-game may be slightly different than what is calculated.
It is important to understand that most champion statistics that stack multiplicatively are displayed as the opposite of the actual numbers that are multiplied. For example, 10% damage reduction should instead be understood as 90% damage taken, and 25% damage reduction should instead be understood as 75% damage.
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- Example: If your champion has armor granting 10% damage reduction and an item granting 10% damage reduction, you multiply the damage factors—0.9 and 0.9—to get 0.81, which means your champion has 19% damage reduction (against physical damage).
Effects that stack multiplicatively
- Attack speed reduction
- Armor penetration, percent
- Armor reduction, percent
- Damage reduction†
- Magic penetration, percent
- Magic resistance reduction, percent
- Crowd control reduction
- Note that all sourced from items will not stack as they share the same named item effect.
† Armor and magic resistance each contribute a single percentage value to the larger category of "damage reduction." Calculate the final percentage of each before combining with other sources of damage reduction.
Special stacking
Please visit the respective articles for details on these statistics stack: