More specifically:
In Gen IV, Simple causes the multipliers for each stage to be boosted; that is, a +1 will always be x2 instead of x1.5, a +2 will always be x3 instead of x2, etc. This means that using, say, Amnesia, will still boost Sp.Def by two stages, but the multiplier associated with two stages is now x3 instead of x2.
In Gen V, Simple instead causes the actual boosts to be doubled. A +1 is still x1.5, a +2 is still x2, etc. This means that using Amnesia will now boost Sp.Def by four stages, using the standard four stage multiplier of x3.
This change means that Baton Pass boosts are no longer effectively doubled when passing to a Simple user in Gen V.