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Multipliers

Difficulty | Dmg Done | Dmg Taken
------------------------------------------
V.easy     | x 2      | x 0.5
Easy       | x 1.5    | x 0.75
Normal     | x 1      | x 1
Hard       | x 0.75   | x 1.5
V.Hard     | x 0.5    | x 2
Survival   | x 0.5    | x 2

Not sure about the # for NPC's HP increase.

It also affect some other things, like the Healing speed/rate, spawn rate of legendary enemies and other similar effects. I don't have hard numbers for those though. There are no new mechanics on higher difficulty.