Stack is used as a noun and a verb in Diablo terminology.
The most basic meaning is to add up more than one of the same effect or item. Thus a character needs a "stack" of 27 Flawless Square Emeralds to upgrade to a Star Emerald. Stack can also refer to multiple types of damage or other effects adding up. "Those new gloves really helped to stack up my damage." Or the negative, "Two of the same type of shrine just resets the bonus, rather than stacking it up double."
Stacks is often used as a noun to refer to the levels of a skill or other game feature that can add the same bonus a number of times. Thus skills like Frenzy can stack up to five times and Sweeping Wind up to three times, each one adding arithmetically to the total value. There are many other such examples.
The most common "stacks" in the game are those from Nephalem Valor, which stack up to five times for a total boost of 75% Magic Find, Gold Find, and % Experience gained.
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