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Simple doubles the effectiveness of stat modifiers.

Gen IV

Simple doubles the effectiveness of stat modifiers. For example, if Defense Curl is used, the user's Defense stat will increase by one stage, but the effect of that stage is equal to the change of two stages. Similarly, if Tail Whip is used against this Pokémon, its Defense stat will fall one stage, but be treated as two.
However, stat modifiers are still effectively capped at six stages; a Simple Pokémon with +3 or -3 in a stat can still increase or decrease the stage of that stat, but those changes will have no effect on the actual stats of the Pokémon.

A Pokémon that uses Psych Up on a target with Simple only copies the actual (not effective) stage changes.

Gen V

Simple now doubles the number of stages in a stat change rather than doubling the effectiveness of each boost. This means that moves like Defense Curl can only be used three times before failing (unlike Generation IV, where it could be used six times, but only have effect up to the third).

As the effective stat change is now the same as the actual number of stages a stat is changed, using Psych Up on a target with Simple behaves as expected, copying twice the number of stat boosts compared to if the Psych Up user had used the stat boosting moves themselves. This also means that using Baton Pass with a Simple Pokémon as the recipient will no longer effectively double the stat changes that are transferred.
The move Simple Beam can change the target Pokémon's Ability to Simple.

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So MANY words, my answer is simple... get it LOL (i said simple and the move is simple)
It doubles the amount of stages that moves & abilities lower and raise stats. Defense Curl raises Defense by 1 stage, but under Simple, 2 stages. Swords Dance + 2. Under Simple, +4