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.