Any buff that has "levels". Each level is a stack. Example: Aetherflow can have up to 3 levels or stacks. Some actions will use an Aetherflow stack or level. When the stack reaches zero, you lose Aetherflow and any spells or bonuses that require it. MNK has Greased Lightning stacks that improve their attack speed and dmg I think. WARs have Defiance stacks that has 5 levels. Each stack increases Crit rate and at 5 stacks, WARs can unleash a special ability that spends all 5 stacks.

Stacks also refer to buffs/debuffs. Example, a WHM and SCH both have access to Aero. Aero stacks which means when both WHM and SCH cast it, the mob has 2 instances of Aero because it stacks.